Calculating load resistor for maximum power
Find the Thévenin voltage and resistance as usual (with RL disconnected, looking into A and B). 

Then calculate the power dissipation in the load resistor as a function of the load resistance. 

Differentiate that equation and set to zero to find the maxima (or minima, but it will be a maxima). 

Here is a plot of the function (arbitrary values of source resistance and voltage and range of load resistance)-  power on the Y axis, load resistance on the X axis: