Quadrilateral a′b′c′d′ is a dilation of abcd about point f. what is the scale factor?

Since you didn't give the diagram, we can't find the exact answer. However, I can give you some guidance so you can find the correct answer.

You are looking for the value that you multiply to get from the first shape to the second. Just write and solve an equation with k as the scale factor.

Here is an example of a dilation from 5 to 20.

5k = 20    Divide both sides by 5
k = 4