Question 850245
Let w = width.
Length is {{{w+15}}}.
Garden area is {{{w(w+15)}}}.


The sidewalk forms an outer area and an inner area.
The outer area is {{{(w+2*4)(w+15+2*4)=(w+8)(w+23)}}}.


The sidewalk area is the outer area minus the inner(garden) area, and this area is given:
{{{highlight_green((w+8)(w+23)-w(w+15)=632)}}}.
This is a quadratic equation just requiring some simplification and then finish with either factoring or general solution to a quadratic equation.
You take it from here.