Here's a better approach...
Combination of 4 and 2 will give a product of eight. So if we find the max. no. of pairs of 4 and 2 we can find the max. of x.
Now the no. of 4's that we can extract out of 16! is less than the the no. of 2's. In other words 2's are available in plenty in comparison to 4's. So our answer gets further restricted to the max. no.s of of 4's.
Now the no. of 4's is given by the 16/4 = 4 and 16/ 4^2 =1