Answer
$y=-3$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt{y+4}+6=7
$, is equivalent to
\begin{array}{l}
\sqrt{y+4}=7-6
\\\\
\sqrt{y+4}=1
.\end{array}
Raising both sides to the $\text{
2nd
}$ power, the solution to the equation above, $
\sqrt{y+4}=1
$, is
\begin{array}{l}
y+4=1
\\\\
y=1-4
\\\\
y=-3
.\end{array}
Upon checking, $
y=-3
$ satisfies the given equation.