Find x in the triangle

$\triangle {ACF}$ is similar to $\triangle {DGF}$ . Therefore $|\overline {AF}|\times |\overline {FD}|=4\times {(4+x)}=16+4x$ . Also, $\triangle {ABD}$ is similar to $\triangle {DBF}$ . Therefore $|\overline {AF}|\times |\overline {FD}|=6\times 6=36$ . From this we get $x=|\overline {CG}|=\dfrac{36-16}{4}=\boxed 5$