What values of x will make DE || AB in the given figure?

If $D E \| A B$, then

$\frac{C E}{C B}=\frac{C D}{A C}$

$\frac{x}{x+3 x+4}=\frac{x+3}{4 x+22}$

$\frac{x}{4 x+4}=\frac{x+3}{4 x+22}$

$x \times(4 x+22)=x+3 \times(4 x+4)$

$4 x^{2}+22 x=4 x^{2}+12 x+4 x+12$

$22 x=16 x+12$

$22 x-16 x=12$

$6 x=12$

$x=\frac{12}{6}$

$x=2$

Hence, the value of $x$ is 2 .