F(x) = -4x² + 16 x - 8

The x-value of the vertex can be found by using the formula: -b/(2a).

For this problem, a = -4, b = 16, and c = -8.

x-value = -b/(2a) = -16/(2·-4) = -16/-8 = 2

If x = 2, F(2) = -4(2)² + 16(2) - 8 = 8

So, the vertex is (2, 8).

The equation of the line of symmetry is the equation of the vertical line that passes through the vertex. This equation is: x = 2.