Step 1: Understanding the Concept
Photons are emitted when electrons move from a higher energy level to a lower energy level.
Step 2: Evaluation
The energy difference (and thus frequency) is largest for transitions ending at $n=1$ in the Bohr model.
Step 3: Comparison
Transition from $n=2$ to $n=1$ involves a larger energy gap than $n=6$ to $n=2$.
Hence, the Answer is: (b)