Answer
$x=9$ feet.
Work Step by Step
The area of the empty space in addition to the shaded area is $10(x+6)=10x+60$.
The area of the empty space alone is $6(10-x)=60-6x$
Therefore, the area of the shaded area is $(10x+60)-(60-6x)$.
This also equals $144$ square feet, so $16x=144$, and $x=\frac{144}{16}=9$ feet.
