How to find the load resistor's resistance?
The &quot;maximum power transfer theorem&quot; tells you that for maximum power transfer, the load resistance must be the same as the source resistance.
You've used Thevenin's theorem to find the source resistancee.  Given that and the statement above about the maximum power transfer theorem, you should be able to figure out \$R_{Load}\$ pretty easily.
From that you can find the current through the circuit and the current through \$R_{Load}\$.
With the current through \$R_{Load}\$, you can find the dissipated power using the formula for Joule heating.  That's \$P_{Load} = I_{Load}^2R_{Load}\$