Separate the sentence into parts.

A number squared:  $\displaystyle x^2$

Sixteen less than a number squared:  $\displaystyle x^2-16$

Note that the number 16 is subtract from $\displaystyle x^2$ if 16 is less than the number.

The answer is:  $\displaystyle x^2-16$

"The sum of a number and two thirds" is the result of adding $\displaystyle x$ and $\displaystyle \frac{2}{3}$:

$\displaystyle x+ \frac{2}{3}$

Nine multiplied by this, remembering to use parentheses to override the precedence of multiplication, is:

$\displaystyle 9 \left ( x+\frac{2}{3}\right )$

"The product of seven tenths and a number" is the result of multiplying $\displaystyle \frac{7}{10}$ and $\displaystyle x$:

$\displaystyle \frac{7}{10}x$.

"Twenty added to" this is 

$\displaystyle \frac{7}{10}x+20$

$\displaystyle \frac{2}{3} (x-7)$ is two thirds multiplied by $\displaystyle x-7$, which is the difference of a number and seven. Putting this together, this expression is stated as:

"Two thirds multiplied by the difference of a number and seven"

If we call this unknown number $\displaystyle x$, then "the sum of an unknown number and twelve" is

$\displaystyle x+12$

"seven...multiplied by the sum of an unknown number and twelve" is seven multiplied by $\displaystyle x+12$; remembering to override the order of operations with parentheses, the expression is 

$\displaystyle 7(x+12)$

The result is four times that unknown number, which is 

$\displaystyle 4x$

Putting it together, the equation is

$\displaystyle 7(x+12) = 4x$

Split the sentence into parts.  Let a variable be the number.

Twice a number: $\displaystyle 2x$

The quantity of twice a number squared:  $\displaystyle (2x)^2$

One more than the quantity of twice a number squared: $\displaystyle (2x)^2+1$

The answer is:  $\displaystyle (2x)^2+1$

Separate the sentence into parts.  Use a variable to denote the number.

Half a number:  $\displaystyle \frac{1}{2}x$

Four less than half a number:  $\displaystyle \frac{1}{2}x-4$

The answer is:  $\displaystyle \frac{1}{2}x-4$

Separate the sentence into parts.

Twice a number:  $\displaystyle 2x$

Five more than twice a number:  $\displaystyle 2x+5$

Is nine:  $\displaystyle =9$

Combine the parts.

The answer is:  $\displaystyle 2x+5=9$

Seperate the sentence into parts.

Twice a number:  $\displaystyle 2x$

The cube root of twice a number:  $\displaystyle \sqrt[3]{2x}$

Six more than the cube root of twice a number:  $\displaystyle \sqrt[3]{2x}+6$

The answer is:  $\displaystyle \sqrt[3]{2x}+6$

If we call this unknown number $\displaystyle x$, then "the product of one-tenths and a number" is $\displaystyle \frac{1}{10}x$.

"The product of one-tenths and a number...subtracted from six" is $\displaystyle \frac{1}{10}x$ subtracted from six, or 

$\displaystyle 6 - \frac{1}{10}x$.

This result is equal to seven more than that number, which is $\displaystyle x+7$, so the equation is

$\displaystyle 6 - \frac{1}{10}x = x + 7$.