jmc

The vertex of the parabola is $(-4,2)$, so the equation of the parabola is of the form $$x=a(y-2{)}^2-4.$$The parabola passes through the point $(-2,4)$. Substituting these values into the equation above, we get $$-2=a(4-2{)}^2-4.$$Solving for $a$, we find $a=1/2$. Hence, the equation of the parabola is given by $$x=\frac{1}{2}(y-2{)}^2-4=\frac{1}{2}(y^2-4y+4)-4=\frac{1}{2}{y}^2-2y-2.$$The answer is $\boxed{-2}$.

Alternatively, the value of $x=a{y}^2+by+c$ is $c$ when $y=0$. The parabola passes through the point $(-2,0)$, so $c=\boxed{-2}$.