Four Fours/Lemmata/Two Fours/64/Solutions/6

Solution

 * $64 = 4^{\sqrt {\map {\pi} {4!} } }$

where $\map \pi \cdot$ represents the prime-counting function.

Proof
The primes less than $4! = 24$ are:
 * $2, 3, 5, 7, 11, 13, 17, 19, 23$

so $\map {\pi} {4!} = 9$.

Thus:
 * $4^{\sqrt {\map {\pi} {4!} } } = 4^{\sqrt 9} = 64$