(a) The system is in equilibrium so

∑Torques about any point = 0

Clockwise Torques + Anticlockwise Torques = 0.

Taking Torgues at X

τ_{clockwise}+ τ_{anticlockwise} = 0

[-(m_{1}g X 2m)] + [-(m_{2}g X 16m)] + (F X 14)] = 0

14 F - (100N X 2m) -(300N X 16m) = 0

14F = 4800 + 200

F = 357N