a.  $\sqrt{x^{2}}=7=>\left | x \right |=7=> x=\pm 7$

b.  $\sqrt{x^{2}}=\left | -8 \right |=>\left | x \right |=8=>x=\pm 8$

c.  $\sqrt{4x^{2}}=6<=>\sqrt{(2x)^{2}}=6$

=>  $\left | 2x \right |=6=> 2x=\pm 6=> x=\pm 3$

d.  $\sqrt{9x^{2}}=\left | -12\right |<=> \sqrt{(3x)^{2}}=12$

=>  $\left | 3x \right |=12=> 3x=\pm 12=> x=\pm 4$