Given that P = [[2, 1], [5, -3]] and Q = [[4, -8], [1, -2]], find (2P - Q).

Multiply each element of matrix $P$ by 2.

$$2P = 2 \times \begin{pmatrix} 2 & 1 \\ 5 & -3 \end{pmatrix} = \begin{pmatrix} 2 \times 2 & 2 \times 1 \\ 2 \times 5 & 2 \times (-3) \end{pmatrix} = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix}$$

Subtract the corresponding elements of matrix $Q$ from $2P$.

$$2P - Q = \begin{pmatrix} 4 & 2 \\ 10 & -6 \end{pmatrix} - \begin{pmatrix} 4 & -8 \\ 1 & -2 \end{pmatrix}$$ $$2P - Q = \begin{pmatrix} 4 - 4 & 2 - (-8) \\ 10 - 1 & -6 - (-2) \end{pmatrix}$$ $$2P - Q = \begin{pmatrix} 0 & 2 + 8 \\ 9 & -6 + 2 \end{pmatrix}$$ $$2P - Q = \begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}$$

The calculated matrix $\begin{pmatrix} 0 & 10 \\ 9 & -4 \end{pmatrix}$ matches option D.

The final answer is $\text{D}$.