A prime implicant is a rectangle of 1, 2, 4, 8... or X’s not included in any one larger rectangle. Thus, from the point of view of finding prime implicants, X’s (don’t cares) are treated as 1’s.

Here the ones in RED and GREEN color are the PIs.

An essential prime implicant is a prime implicant that covers at least one 1 that is not covered by any other prime implicant. Don’t cares (X’s) do not make a prime implicant essential.

The 1's marked by STAR can't be covered by any other PI. So the PI to which they belong are EPIs. They are 2 in number.

The larger rectangle of size 4 shouldn't be counted as an EPI because all the 1's are already covered by other PIs (marked by GREEN). The don't cares are not covered but that is not what we see while checking for EPI.

You may be having a doubt that the 1's in 4 sized rectangle are not covered by max sized PI so that should also be EPI but EPI is not defined in such a way. Please refer the link below. I actually didn't know this and thought no. of EPI is 3 but going by the definition and the link I got to know this now.

EPI=2 ( the solution given by ME is wrong i guess :/ )

@Balaji , if you are not convinced , then you can use Quine–McCluskey algorithm . This is also a method to find EPIs. it will take 5-10 minutes but will give the answer as 2.