#### Answer

$P=17\frac{5}{6} \text{ inches}$

#### Work Step by Step

The perimeter $P$ of a rectangle is given by the formula $P=2(L+W)$ where $L$=length and $W$= width.
Use the formula above to obtain:
$P=2(6\frac{1}{4}+2\frac{2}{3})
\\P=2(\frac{4(6)+1}{4}+\frac{3(2)+2}{3})
\\P=2(\frac{25}{4} + \frac{8}{3})$
Make the fractions similar using their LCD of $12$ to obtain:
$\require{cancel}
P=2\left(\frac{25(3)}{4(3)}+\frac{8(4)}{3(4)}\right)
\\P=2\left(\frac{75}{12}+\frac{32}{12}\right)
\\P=2\left(\frac{75+32}{12}\right)
\\P=2(\frac{107}{12})
\\P=\cancel{2}(\frac{107}{\cancel{12}6})
\\P=\frac{107}{6}
\\P=17\frac{5}{6} \text{ inches}$