first of all, let's just deal with the negative so it doesn't mess us up at the final answer. Pos×neg×neg×neg is going to be neg (an odd number of negatives will be negative).
If you know how to cancel, you can do that and make your life easier. But cancelling is REALLY just dividing. Generally, you can multiply fractions by multiplying all the top numbers together and put that on top. And multiply all bottom numbers together and put that on the bottom. But then you have to simplify. See image.
16 people would be at the dinner because Jim and Sarah invited 7 friends and each friend brought 1 guest, so you do 7*2=14 and the 14 + Jim and Sarah=16 people.