Given vectors a = 2 4 and b = -3 4 , find the magnitude of vector a - 2b.

The magnitude of a vector $\begin{pmatrix} x \\ y \end{pmatrix}$ is $\sqrt{x^2 + y^2}$.

$$|a - 2b| = \left| \begin{pmatrix} 8 \\ -4 \end{pmatrix} \right| = \sqrt{8^2 + (-4)^2}$$ $$|a - 2b| = \sqrt{64 + 16} = \sqrt{80}$$ $$|a - 2b| = \sqrt{16 \times 5} = 4\sqrt{5}$$

The value of $|a - 2b|$ is $\boxed{\mathbf{4\sqrt{5}}}$.