A body of mass 14 kg initially at rest explodes and breaks into...

From mass ratio 2:2:3 with total mass 14 kg: individual masses are 4 kg, 4 kg, and 6 kg.
Setting coordinate axes along the motion directions of the two equal fragments: fragment 1 has momentum $\vec{p_1} = 4 \times 18\hat{i} = 72\hat{i}$ kg⋅m/s, and fragment 2 has $\vec{p_2} = 4 \times 18\hat{j} = 72\hat{j}$ kg⋅m/s.
By momentum conservation, initially at rest: $\vec{p_1} + \vec{p_2} + \vec{p_3} = 0$, so $\vec{p_3} = -72\hat{i} - 72\hat{j}$ kg⋅m/s.
Velocity of 6 kg fragment: $\vec{v_3} = \frac{\vec{p_3}}{6} = -12\hat{i} - 12\hat{j}$ m/s.
Speed: $|\vec{v_3}| = \sqrt{144 + 144} = \sqrt{288} = 12\sqrt{2}$ m/s.