To find the value of \( n \) given the equation \( (8n)^\circ = 48^\circ \), we can set up the equation:
\[ 8n = 48 \]
Now, we can solve for \( n \) by dividing both sides by 8:
\[ n = \frac{48}{8} \]
Calculating the right side gives us:
\[ n = 6 \]
Thus, the value of \( n \) is:
\[ \boxed{6} \]