Description of Problem 514: The problem statement shows a sketch of a simply supported beam. The beam is subject to some external loads. You are asked to obtain the maximum bending moment within the beam.
Analysis of Problem 514: Here you just have to draw the shear force diagram and then the bending moment diagram for the beam. Once you have these diagrams you locate where the maximum bending moment occurs. The most efficient way to do this is with the graphical approach you learned back in the day in engineering school. This approach is reviewed well in the Mechanical Engineering Review Manual by M. Lindeburg, and also in any Strength of Materials textbook (e.g., Mechanics of Materials by R.C. Hibbeler). Here's a similar problem that is a little more challenging than Problem 514, yet it is not harder than anything you did in school:
Mechanical Systems and Materials Depth (PM) Exam Sample Problem #3
Post C-D is fixed to beam A-B as shown. The length d of post C-D is such that the system is in static equilibrium.