To find the radius of the circle described by the equation, we start with the given equation:
\[ (x - 6)^2 + (y - 4)^2 - 64 = 0 \]
We can rearrange this equation to isolate the circle on one side:
\[ (x - 6)^2 + (y - 4)^2 = 64 \]
This equation is now in the standard form of a circle, which is:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle, and \(r\) is the radius.
From the equation \((x - 6)^2 + (y - 4)^2 = 64\), we can identify:
- \(h = 6\)
- \(k = 4\)
- \(r^2 = 64\)
To find the radius \(r\), we take the square root of \(r^2\):
\[ r = \sqrt{64} = 8 \]
Thus, the radius of the circle is:
\[ \boxed{8} \]