Step 1 :

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

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(From the results of http://www.mathskey.com/question2answer/31696/thevenin-problem&
\ http://www.mathskey.com/question2answer/31695/thevenin-problem).
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\"\"

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Observe the diagram.

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The resistors are connected in seies.

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\"\"

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Thevenin\"\"s voltage is \"\".

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Circuit current is  \"\".

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Substitute corresponding values in the above equation.

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\"\"

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Step 2 :

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

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Maximum power dissipated is \"\".

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

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\"\"

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Maximum power dissipated is \"\".

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Solution :

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Maximum power dissipated is \"\".