I like Sudharaka's solution, but here is an alternative approach just to show there is more than one way. Let H be the number of heads, T the number of tails. Then
P(H < T) + P(H = T) + P(H > T) = 1
By symmetry, P(H < T) = P(H > T), so
2 P(H > T) + P(H = T) = 1
It's pretty easy to find P(H = T) because this is just the case H = T = 4. Then use the equation above to solve for P(H > T).