In the exponential function \( y = 8(6^x) \), the function grows exponentially as \( x \) increases.
For exponential functions of the form \( y = ab^x \) where \( a > 0 \) and \( b > 1 \), the horizontal asymptote is determined by the behavior of the function as \( x \) approaches negative infinity.
As \( x \to -\infty \), \( 6^x \) approaches 0. Therefore, \( y = 8(6^x) \) approaches \( 8 \cdot 0 = 0 \).
Thus, the horizontal asymptote is:
\[ y = 0 \]
So the correct answer is \( \mathbf{y = 0} \).