We are given the polynomial function $h(x) = 2x^4 - x^3 + 2x^2 - 6x - 5$, and we are asked to evaluate $h(-2)$.

1. Problem Description

We are given the polynomial function $h(x) = 2x^4 - x^3 + 2x^2 - 6x - 5$, and we are asked to evaluate $h(-2)$.

2. Solution Steps

We substitute $x = -2$ into the polynomial:

$h(-2) = 2(-2)^4 - (-2)^3 + 2(-2)^2 - 6(-2) - 5$

$h(-2) = 2(16) - (-8) + 2(4) - (-12) - 5$

$h(-2) = 32 + 8 + 8 + 12 - 5$

$h(-2) = 40 + 8 + 12 - 5$

$h(-2) = 48 + 12 - 5$

$h(-2) = 60 - 5$

$h(-2) = 55$

3. Final Answer

The final answer is 55.