#### Answer

$2\textbf{u} + 3\textbf{v} = \langle -4, 14 \rangle$

#### Work Step by Step

$2\textbf{u} + 3\textbf{v} = 2\langle4,-2\rangle + 3\langle-4,6\rangle = \langle8,-4\rangle + \langle-12,18\rangle = \langle 8 - 12, -4 + 18\rangle = \langle -4, 14 \rangle$