Answer
$$\langle0,-14\rangle$$
Work Step by Step
To scale a vector in component form, multiply each component by the scale factor.
$$2\vec{v}=2\langle 4,-3\rangle=\langle 2\times 4,2\times (-3)\rangle=\langle8,-6\rangle$$
$$4\vec{w}=4\langle 2,2\rangle=\langle 4\times 2,4\times 2\rangle=\langle8,8\rangle$$
To subtract vectors in component form, subtract x and y components separately.
$$2\vec{v}-4\vec{w}=\langle 8,-6\rangle-\langle 8,8\rangle=\langle 8-8,-6-8\rangle=\langle0,-14\rangle$$
