The expression can be simplified: (x^2+1/x)^12=(x^2(1+x^-3))^12=x^24(1+x^-3)^12. The coefficient of x^0 is found by working out when x^-3 becomes x^-24 to counterbalance x^24. (x^-3)^8. The next thing to do is to work out how far along the expansion we have to go: 1 12 12*11/2 etc. are the coefficients in sequence. There are 13 coefficients, starting and ending with 1, and, using Pascal's triangle, we know that the sequence is palindromic, that is, there is a sort of reflection of the coefficients. The 12th row of Pascal's triangle is 1, 12, 66, 220, 495. Stop! 495 is also the coefficient of x^-24. So 495 (=12*11*10*9/4!) is what we're looking for.