Help with DC circuit theory problem
Hint #1: You need to work with the Thevenin equivalent looking into nodes A and B from \$R_P\$.

Hint #2: What is the condition for maximum power transfer? (\$R_L =\ ?\$)

Hint #3: You know the total current through \$R_{Th}\$ and \$R_P\$ as well as the total voltage across both.