How do you know if it is a adding or subtraction problem when you combine like terms?

You look at the sign behind the second term. Here are some examples ...

2x + 8 - 4x

You are going to subtract 2x - 4x because there is a negative sign behind the 4x.

8y + 1 + y

You are going to add 8y + y because there is a positive sign behind the y.

4 + 2x - 5 + 7x

You are going to subtract 4 - 5 because there is a negative sign behind the 5.

You are going to add 2x + 7x because there is a positive sign behind the 7x.