Answer
False.
Work Step by Step
The given equation is
$\Rightarrow \sqrt{x+6}=x+2$
Square both sides.
$\Rightarrow (\sqrt{x+6})^2=(x+2)^2$
Use the special formula $(A+B)^2=A^2+2AB+B^2$
We have $A=x$ and $B=2$
$\Rightarrow x+6= (x)^2+2(x)( 2)+(2)^2$
Simplify.
$\Rightarrow x+6= x^2+4x+4$
Hence, the given statement is false.