Question 120170
First let's draw a picture. We can see that the length of the large rectangle is  {{{6+2x}}} and the width of the large rectangle is {{{4+2x}}} since we are adding {{{2x}}} to both the length and the width. note: the inner blue rectangle is the garden

{{{drawing(500,500,-10,7,-7,7,
blue(line(-5,3,5,3)),
blue(line(5,3,5,-3)),
blue(line(5,-3,-5,-3)),
blue(line(-5,-3,-5,3)),
red(line(-6,4,6,4)),
red(line(6,4,6,-4)),
red(line(6,-4,-6,-4)),
red(line(-6,-4,-6,4)),
green(line(-5,3,-5,4)),
green(line(-5,3,-6,3)),
green(line(5,3,5,4)),
green(line(5,3,6,3)),
green(line(-5,-3,-5,-4)),
green(line(-5,-3,-6,-3)),
green(line(5,-3,6,-3)),
green(line(5,-3,5,-4)),
red(locate(-0.5,4.5,Length:6+2x)),
blue(locate(-0.5,3.5,Length:6)),
red(locate(-8.95,0,Width:4+2x)),
blue(locate(-7.05,1.2,Width:4)),
green(locate(-4.8,3.8,x)),
green(locate(-5.6,3,x))
)}}}



From the drawing, we can see that the area of the small rectangle is: {{{A=L*W=6*4=24}}}



Also, from the drawing, the area of larger rectangle is:


{{{A=(6+2x)(4+2x)}}}



Now since we only want the area of the walkway, just subtract the area of the garden from the larger rectangle's area to get 



{{{A=(6+2x)(4+2x)-24}}}



Now since the area of the walkway is the same as the garden, this means {{{A=24}}}


{{{24=(6+2x)(4+2x)-24}}} Plug in {{{A=24}}}




{{{24=4x^2+20x+24-24}}} Foil



{{{0=4x^2+20x+24-24-24}}} Subtract 24 from both sides



{{{0=4x^2+20x-24}}} Combine like terms




{{{4(x+6)(x-1)=0}}} Factor the right side 




Now set each factor equal to zero:

{{{x+6=0}}} or  {{{x-1=0}}} 


{{{x=-6}}} or  {{{x=1}}}    Now solve for x in each case



So our possible answers are 

 {{{x=-6}}} or  {{{x=1}}} 



However, since a negative length doesn't make sense, our only solution is {{{x=1}}} 



So the walkway's width is 1 meter