Given the function $y = -x^2 - 6x + k$ and the maximum value is 2:

1. Find the vertex: $x = -\frac{b}{2a} = -\frac{-6}{2(-1)} = -3$

2. Substitute $x = -3$ into the function to find $y$: $y = -(-3)^2 - 6(-3) + k = -9 + 18 + k = 9 + k$

3. Given that the maximum value is 2: $9 + k = 2$

4. Solve for $k$: $k = 2 - 9 = -7$

Thus, the value of $k$ is $-7$.