The vertices of ABC are A(4, -4), B(8, -8) and C(4, -8). Find the image of ABC under a reflection in the x-axis followed by a reflection in the y-axis.

$$C_1 = (4, -(-8)) = (4, 8)$$

The vertices of $\triangle A_1B_1C_1$ are $\boxed{A_1(4, 4), B_1(8, 8), C_1(4, 8)}$.

$$C_2 = (-4, 8)$$

The vertices of $\triangle A_2B_2C_2$ are $\boxed{A_2(-4, 4), B_2(-8, 8), C_2(-4, 8)}$.

d) To find the image $\triangle A_3B_3C_3$ of $\triangle A_2B_2C_2$ under a reflection in the line $y=2$, we use the transformation rule $(x, y) \to (x, 2k - y)$, where $k=2$. So the rule is $(x, y) \to (x, 2(2) - y) = (x, 4 - y)$.

$$C_3 = (-4, 4 - 8) = (-4, -4)$$

The vertices of $\triangle A_3B_3C_3$ are $\boxed{A_3(-4, 0), B_3(-8, -4), C_3(-4, -4)}$.