Question 340744
First, re-write the equation for clarity
{{{sqrt(x+6) + sqrt(2-x) = 4}}}
and square both sides
{{{x+6 + 2-x + 2sqrt((x+6)(2-x)) = 16}}}
simplify
{{{sqrt((x+6)(2-x)) = 4}}}
and square both sides
{{{(x+6)(2-x) = 16}}}
multiply
{{{2x - x^2 + 12 -6x  = 16}}}
simplify
{{{x^2 + 4x + 4 = 0}}}
notice that the equation is
{{{(x+2)^2 = 0}}}
i.e.
{{{x = -2}}}
So the answer is D

In general you get rid of the radicals and solve the resulting equation.
When the equation cannot be easily solved, try to guess the rational roots
and simplify the equation.