See the explanation below.
Work Step by Step
Standard form of a parabola is $x=a(y-k)^2+h$ and Here, vertex:$(h,k) or (k,h) $ In order to get the vertex we will have to arrange the equation in the standard form of a parabola, for this need to complete the square for $y^2$. For example: Since we are given $x=-2y^2+4y+6$ It can be written as: $x=-2y^2+4y+6$ or, $x=-2(y^2-2y+1)+6+2$ or, $x=-2(y-1)^2+8$ ; complete the square for $y^2$ Compare the given equation with the standard form. Thus, vertex: $(8,1)$