To find the value of \( n \) in the equation that states \( (8n)^\circ \) and \( 48^\circ \) are equal, we can set up the equation:
\[ 8n = 48 \]
Now, solve for \( n \) by dividing both sides by 8:
\[ n = \frac{48}{8} = 6 \]
Thus, the value of \( n \) is
\[ \boxed{6} \]