In order to solve this problem, we need to start at $\displaystyle -6$ on the number line. 

Next, we have $\displaystyle +6$ which means we need to move $\displaystyle 6$ places to the right on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 6$ places to the right, and ended at $\displaystyle 0$; thus,

$\displaystyle -6+6=0$

Remember, $\displaystyle -6$ and $\displaystyle 6$ are opposite numbers. A number and its opposite always have a sum of $\displaystyle 0$. 

In order to solve this problem, we need to start at $\displaystyle -3$ on the number line. 

Next, we have $\displaystyle -5$ which means we need to move $\displaystyle 5$ places to the left on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 5$ places to the left, and ended at $\displaystyle -8$; thus,

$\displaystyle -3-5=-8$

In order to solve this problem, we need to start at $\displaystyle -12$ on the number line. 

Next, we have $\displaystyle -4$ which means we need to move $\displaystyle 4$ places to the left on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 4$ places to the left, and ended at $\displaystyle -16$; thus,

$\displaystyle -12-4=-16$

In order to solve this problem, we need to start at $\displaystyle -11$ on the number line. 

Next, we have $\displaystyle -3$ which means we need to move $\displaystyle 3$ places to the left on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 3$ places to the left, and ended at $\displaystyle -14$; thus,

$\displaystyle -11-3=-14$

In order to solve this problem, we need to start at $\displaystyle 4$ on the number line. 

Next, we have $\displaystyle -11$ which means we need to move $\displaystyle 11$ places to the left on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 11$ places to the left, and ended at $\displaystyle -7$; thus,

$\displaystyle 4-11=-7$

In order to solve this problem, we need to start at $\displaystyle 9$ on the number line. 

Next, we have $\displaystyle -13$ which means we need to move $\displaystyle 13$ places to the left on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 13$ places to the left, and ended at $\displaystyle -4$; thus,

$\displaystyle 9-13=-4$

In order to solve this problem, we need to start at $\displaystyle -3$ on the number line. 

Next, we have $\displaystyle -10$ which means we need to move $\displaystyle 10$ places to the left on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 10$ places to the left, and ended at $\displaystyle -13$; thus,

$\displaystyle -3-10=-13$

In order to solve this problem, we need to start at $\displaystyle -10$ on the number line. 

Next, we have $\displaystyle +10$ which means we need to move $\displaystyle 10$ places to the right on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 10$ places to the right, and ended at $\displaystyle 0$; thus,

$\displaystyle -10+10=0$

Remember, $\displaystyle -10$ and $\displaystyle 10$ are opposite numbers. A number and its opposite always have a sum of $\displaystyle 0$. 

In order to solve this problem, we need to start at $\displaystyle -15$ on the number line. 

Next, we have $\displaystyle +5$ which means we need to move $\displaystyle 5$ places to the right on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 5$ places to the right, and ended at $\displaystyle -10$; thus,

$\displaystyle -15+5=-10$

In order to solve this problem, we need to start at $\displaystyle -11$ on the number line. 

Next, we have $\displaystyle +7$ which means we need to move $\displaystyle 7$ places to the right on the number line. When we have an addition sign  $\displaystyle (+)$ we move to the right because that is towards the positive side of the number line. When we have a subtraction sign $\displaystyle (-)$ we move to the left because that is towards the negative side of the number line. 

The orange arrow moved $\displaystyle 7$ places to the right, and ended at $\displaystyle -4$; thus,

$\displaystyle -11+7=-4$