If E[X^r] = 6^r
where r = 1, 2, 3...
can you please help me find the moment generating function and the p.m.f. of X?
and you should recognise what this function is. Then it should be clear that is the mgf of a pmf that has all its mass concentrated at one point. That is, p(x) = 1 when x = c and the value of c is obvious.