Question

What affects the direction of the current moving through a wire? Check all that apply.
-the direction the wire moves in
-the thickness of the wire
-the direction of the magnetic field
-the type of magnet
-the direction of the needle on an ammeter

Answer 1

I am definitely sure that these factors affect the direction of the current moving through a wire: 
the direction the wire moves in
the direction of the magnetic field
the direction of the needle on an ammeter
You can check it by using Right-Hand rule which is very useful when you need to find how charges move.

Answer 2

The two I know is:
-the direction the wire moves in

-the direction of the magnetic field