notice I highlighted "directly"

this means that as the length of a side increases, the diagonal of the octagon increases at a constant amount as well.

Think of a line: y=mx

where y is the diagonal, and x is the side.

thus: y/x=m

now substitute known values: 23/6=m

now that gives equation: y=(23/6)x

now substitute 15 for side length: y=(23/6)(15)=57.5

so the diagonal is 57.5