Solids of Revolution: Washer or Shell Method?

Hello everyone. I have a general question in regards to the washer and shell method. When and how do I know when to use either one? I know HOW to use them - I just need to know when to determine which one to use. For example:

1) Let R be the region bounded by the lines y = 0, y = x, and y = 6-x.

a) Find the volume generated when R is rotated around the line y = -3.

b) Find the volume generated when R is rotated around the line x = 0.

**Again, I don't want the solutions/answers**. I want to know which method to use for each one, and WHY we choose that method as opposed to the other one. I know that in theory, both methods should work, but there are instances where one is clearly easier than the other. That is the concept I am having some difficulty to grasp.