Power of a resistor

The voltage across resistor $R$ and $7\Omega$ resistor is (13-6=7V). The maximum current through the $7\Omega$ resistor is when $R=0$ , then the current through the $7\Omega$ resistor is $=\dfrac {13-6}{7} = 1A$ and the maximum power delivered to the $7\Omega$ resistor $=1^2\times 7 = \boxed{7}W$ .

I solved it a similar way as Chew-Seong, I used Kirchhoff's laws and set up a matrix. The thing is, I didn't fully understand what the question was asking and answered a different question in my tinkering. What I initially thought the question was asking was, What is the value of $R$ , such that the power dissipated by it is maximized? This should be a follow up question.