To solve for \( y \) in the equation
\[ b^4c - 7 = \frac{by}{c} \cdot 7, \]
we can first simplify the right side of the equation:
\[ b^4c - 7 = \frac{7by}{c}. \]
Next, we can multiply both sides by \( c \) to eliminate the fraction:
\[ c(b^4c - 7) = 7by. \]
This simplifies to:
\[ cb^4c - 7c = 7by. \]
Now, we want to isolate \( y \). We can divide both sides by \( 7b \) (assuming \( b \neq 0 \)):
\[ y = \frac{cb^4c - 7c}{7b}. \]
This can be simplified further:
\[ y = \frac{c(b^4c - 7)}{7b}. \]
So, the final expression for \( y \) is:
\[ y = \frac{c(b^4c - 7)}{7b}. \]