Given vector A = (3, 5).

Given vector $A = (3, 5)$.

$$-2A = -2 \times (3, 5) = (-2 \times 3, -2 \times 5) = (-6, -10)$$

Given vector $B = (4, 6)$.

$$3B = 3 \times (4, 6) = (3 \times 4, 3 \times 6) = (12, 18)$$

Add the corresponding components of the resulting vectors.

$$-2A + 3B = (-6, -10) + (12, 18) = (-6 + 12, -10 + 18) = (6, 8)$$

The magnitude of a vector $(x, y)$ is given by the formula $\sqrt{x^2 + y^2}$.

$$||-2A + 3B|| = ||(6, 8)|| = \sqrt{6^2 + 8^2}$$ $$||-2A + 3B|| = \sqrt{36 + 64}$$ $$||-2A + 3B|| = \sqrt{100}$$ $$||-2A + 3B|| = 10$$

The magnitude is $\text{10}$.