There are only 2 real intersection points. To find them, you simply need to find out the x-values where the functions equal each other, or equivalently where the difference between them is 0:
intsx = solve(x^6 == 3^x , x)
intsx = solve(x^6 - 3^x == 0 , x)
giving the 2 real roots:
and 4 complex roots.