Ok, so you know that two diagonals of a rectangle are equal to each other. And you know half of the diagonal is x+2, and the entire diagonal is 4x-16. So here you can just make an equation which will be:
2(x+2)=4x-16
2x+4=4x-16
2x=20
x=10
So to find the entire diagonal just plug x value into one of these and the diagonal will equal 24