network theorem

To maximize power dissipated you need to maximize current, which means you want to minimize resistance.

The variable resistor can apparently me anything from zero to infinity. Setting it to zero results in a total circuit resistance of 3 ohms. Setting it to infinity results in a total circuit resistance of 9 ohms. Which maximizes current at the 3 ohm load?

Raj that's not ordinarily what's meant by "source resistance." In the circuit you've given us the internal resistance of the battery itself would be so-called but given no instruction to the contrary we must consider it zero, in which case of course the load gets most current at zero setting of the pot