Answer
$x = 6$
Work Step by Step
Similar triangles have corresponding sides that are proportional. Let's write a proportion to compare two sides of one triangle to two sides of the other triangle:
$\frac{8}{x} = \frac{2x}{9}$
Cross multiply to get rid of the fractions:
$2x^2 = 72$
Divide each side by $2$:
$x^2 = 36$
Take the square root of $36$ to solve for $x$:
$x = 6$
