The four geometric means between 2 and 64 are 

Step 1: Set up the GP
The sequence is: $2,\ G_1,\ G_2,\ G_3,\ G_4,\ 64$
Total terms $= 6$, so $n = 6$

Step 2: Find common ratio $r$
$a = 2,\ a_6 = 64$

$a_6 = a \cdot r^{n-1}$
$64 = 2 \cdot r^5$
$r^5 = 32$
$r^5 = 2^5$
$r = 2$

Step 3: Find the four geometric means
$G_1 = ar = 2 \times 2 = 4$
$G_2 = ar^2 = 2 \times 4 = 8$
$G_3 = ar^3 = 2 \times 8 = 16$
$G_4 = ar^4 = 2 \times 16 = 32$

Answer: The four geometric means are $\boxed{4, 8, 16, 32}$