Here's a way that doesn't require any magic.
Assume R=0. What is the current and then the total dissipation of R1 and R2.
Power dissipation is proportional to current squared, and this pair of resistors just happens to dissipate 4 times the power that the target R needs to dissipate.
Given that this means the current would halve to make this pair of resistors dissipate 24W, what does that tell you about the value of R and the dissipation it would have?
Simple approaches like this (whilst not generally applicable) can often work well for problems that are designed to have "nice" solutions. At worst, they provide a method to estimate a value or double-check your answer.