F must be first or last, which eliminates one answer. D must come before C, which eliminates another. E must be immediately surrounded by D and C, which eliminates yet another. And the last we take out because A cannot be first.

If Package B is delivered third, then the only place the DEC block can fit is in spots four, five and six, respectively. Therefore we know the only place E could go is in spot five, which means it must be true.

If Package A is delivered second, there are only two spots where the DEC block can fit: either in spots three, four and five, or four, five and six. Leaving us with two possible set ups:

_ A D E C _     OR    _ A _ D E C

Leaving us to place F and B. In the first solution, F and B are interchangeable - since the only rule we are working with is that F must go either first or last. In the second solution, F must go first, leaving us with only one way to solve. Therefore, the following three solution are the only possibilities:

F A D E C B;  B A D E C F;  F A B D E C

If Package C is third, the we know that package D and E must be second and third, respectively.

_ D E C _ _

Package A cannot go first or fifth, so we must place it last.

_ D E C _ A

F must then go first, and we fill in B in the second spot.

F B D E C A

Knowing that Mildred's portrait comes first lets us plot out the possible locations for the Nancy/Quentin block. They can either go in spots three and five or four and six, respectively. (Nancy cannot go in spot two, because Lily has to come before her.) This creates two possibilities for solutions. The first, with Nancy and Quentin in spots three and six gives us Lily in two, and either Peter or Owen in four and the other one in six. The second possibility with Nancy and Quentin in spots four and six gives us the option of Peter, Lily or Owen for spots two and three, and then whomever is left of Peter and Owen for spot five. Therefore, considering both possibilities the only people who could occupy the second spot when Mildred is in the first spot are Owen, Lily and Peter.

If peppers must be on a pizza made after the sausage pizza, then peppers can never be on the first pizza or the same pizza as sausage.  We can also easily eliminate any option in which tomatoes and mushrooms are not paired.  Remember, sausage is only required to be on the second pizza if mushrooms are on the first.

Since peppers must be on a pizza made after the pizza with sausage, peppers must be on the third pizza.  Now, since the second and third pizzas already have one topping each, and since mushrooms and tomatoes must be on the same pizza, they must be on the first pizza.  As a result, anchovies must be on the second pizza because they cannot be on the same pizza as peppers.  The only remaining spot for bacon is on the third pizza.  Therefore, both bacon and peppers must be on the third pizza.

In this scenario, we actually know the toppings on all four pizzas.

Since anchovies are on the second and fourth pizzas, we know that peppers cannot be on the second and fourth pizzas based on our first condition.  Also, peppers have to come after sausage, based on the fourth condition, which means they cannot be first.  Thus, peppers MUST be on the third pizza.

The second condition states that mushrooms and tomatoes MUST be on the same pizza.  At this point, since anchovies are on two pizzas, and peppers on another, the only possible pizza for both mushrooms and tomatoes is the first pizza.  The first pizza is now fully topped.

The third condition states that sausage must be on the second pizza if mushrooms are on the first pizza.  Therefore, sausage must be the second topping on the second pizza.  The second pizza is fully topped.

There are only two spots available, so bacon becomes the second topping on both the third and the fourth pizzas.  So our order must be:

MT, AS, PB, AB

This is an inference we could have made just from the initial set up of this game. Since seniors must always be preceeded by juniors, the first spot must always be a junior. All of the other scenarios are possible and most have been seen in other set ups for other questions.

If Dorian is reading we know Charlie cannot read, so any answer that includes him can be eliminated. Any answer that includes either Ernest or Xue without the other can also be eliminated. Any answer that includes Alan and not Belle is also eliminated. Any answer that includes Belle and Yardley and does not have Belle reading first is also eliminated, leaving only the correct answer.