To find the y-coordinate of the inverse of the point (6, 0) for the function \( g(x) \), we first recognize what the inverse of a point \( (a, b) \) is. The inverse is given by the point \( (b, a) \).
In this case, we have the point \( (6, 0) \). Here, \( a = 6 \) and \( b = 0 \).
Thus, the inverse point would be \( (0, 6) \). Therefore, the y-coordinate of the inverse of the point \( (6, 0) \) is:
\[ \boxed{6} \]