Question 626847
Let {{{x}}} be the width of the garden (in feet).
Since the garden is twice as long as it is wide,
its length must be {{{2x}}}.
With one piece of sidewalk on each side,
the dimensions (in feet) of the garden plus sidewalk are
{{{width=x+4+4=x+8}}} and 
{{{length=2x+4+4=2x+8}}}
It would look like this:
{{{drawing(450,300,-5.5,24.5,-6,14,
rectangle(0,0,16,8),
rectangle(-4,-4,20,12),
arrow(-2.5,4,-4,4), arrow(-1.5,4,0,4),
arrow(8,10.5,8,12), arrow(8,9.5,8,8),
locate(7.8,10.5,4),locate(-2.2,4.5,4),
locate(7.4,1.1,2x),locate(7,-4,2x+8),
locate(15.2,4.5,x),locate(20.1,4.5,x+8)
)}}}
The area (in square feet) of the whole thing is
{{{length*width=(2x+8)(x+8)=2x^2+16x+8x+64=2x^2+24x+64}}}
The area of the garden part only is
{{{(2x)(x)=2x^2}}}
The difference is the area (in square feet) of the sidewalk only,
{{{2x^2+24x+64-2x^2=256}}} --> {{{24x+64=256}}}
Subtracting 64 from both sides of the equal sign we get
{{{24x+64=256}}} --> {{{24x+64-64=256-64}}} --> {{{24x=192}}}
Dividing both sides of the equal sign by 24 we get
{{{24x=192}}} --> {{{24x/24=192/24}}} --> {{{highlight(x=8)}}}
The garden is {{{highlight(8)}}} feet wide, and {{{2x=2*8=highlight(16)}}} feet long