Let's convert the width to an improper fraction first:
[tex]6 \frac{2}{3} =  \frac{6*3+2}{3} =  \frac{20}{3}   [/tex]
This means that the length is:
[tex] \frac{20}{3}*2 =  \frac{40}{3}  [/tex]
The perimeter of a rectangle is:
[tex]2(l+w)[/tex]
Plug in values, and you get:
[tex]2( \frac{40}{3}+ \frac{20}{3}) =  2(\frac{60}{3}) =  \frac{120}{3} = 40    [/tex]
So, your answer is 40 in.