The picture looks like a 
connected sum of 4 tori with two holes. Am I correct or is there any other algorithm that I don't know.
P.S: I am sorry for giving a picture like this but I got this question in an old question paper and didn't get a better way to represent it.
It must be a connected sum of projective planes with a few boundary components. This follows from the classification of compact surfaces and the fact that, in the picture you give, there exists a loop (around one of the half twisted handles) which can not be covered by orientation preserving charts. Hence the whole surface is nonorientable.