The no of sol are in [0.2Pi] such that sin(2x)⁴=1/8

For sin($) = (1/8) => $ = (1/8) (almost)
So, the general solution is (2x)^(4) = 2nπ+(1/8) or (2nπ+1)π-(1/8).
Now, for x in range [0,2π], let us check for the maximum limit, putting x=2π,
(2*2π)^4 = (2nπ+1)π-(1/8) => n = 3968 (the nearest small integer)
Therefore, the total number of solutions is 2*3968 = 7936 (considering the smaller solution as well that we have not checked for as it is small and hence comes under the range)