This is pretty straightforward--just remember the definition of a log:

log_ab=c if a^c = b

Thus the equation can be rewritten as:

2² = log₃(log₄2ⁿ)

Now we invoke the definition again:

3²² = log₄2ⁿ

81 = log₄2ⁿ

4⁸¹ = 2ⁿ

2^2*81 = 2ⁿ

Therefore, n = 2 * 81 = 162