Step 1 :

Redraw the circuit with equivalent thevenin $\"\"$ s voltage and resistance.

(From the results of http://www.mathskey.com/question2answer/31679/thevenin-equivalent-circuit

$\"\"$

Observe the diagram.

The resistors are connected in seies.

$\"\"$

Thevenin $\"\"$ s voltage is $\"\"$

Circuit current is $\"\"$ .

Substitute corresponding values in the above equation.

$\"\"$

Step 2 :

Maximum power will be transferred when source resistance and thevenin $\"\"$ s resistances are equal.

Maximum power dissipated is $\"\"$ .

Substitute $\"\"$ and $\"\"$ in the above equation.

$\"\"$

Maximum power dissipated is $\"\"$ .

Solution :

Maximum power dissipated is $\"\"$ .