1. **State the problem:** We have three forces acting on a body: $$F_1 = 2m + n, \quad F_2 = -3m + 4n, \quad F_3 = 4m - 6n$$ The mass of the body is 12 kg. We need to find the magnitude of the acceleration of the body. 2. **Formula used:** According to Newton's second law, the net force $F_{net}$ acting on a body is related to its mass $m$ and acceleration $a$ by: $$F_{net} = m a$$ Therefore, $$a = \frac{F_{net}}{m}$$ 3. **Calculate the net force:** Sum the forces component-wise: $$F_{net} = F_1 + F_2 + F_3 = (2m + n) + (-3m + 4n) + (4m - 6n)$$ Combine like terms: $$F_{net} = (2m - 3m + 4m) + (n + 4n - 6n) = 3m - n$$ 4. **Find the magnitude of the net force:** The magnitude of a vector $F = am + bn$ is: $$|F| = \sqrt{a^2 + b^2}$$ Here, $$|F_{net}| = \sqrt{3^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$$ 5. **Calculate the acceleration magnitude:** Using mass $m = 12$ kg, $$a = \frac{|F_{net}|}{m} = \frac{\sqrt{10}}{12}$$ 6. **Final answer:** The magnitude of the acceleration is $$a = \frac{\sqrt{10}}{12} \approx 0.263$$ This means the body accelerates at approximately 0.263 units in the direction of the net force.