To find the corresponding y-value when \( x = 4 \) in the function \( y = 4.25(6)^x \), we substitute \( x \) with 4:
\[ y = 4.25(6)^4 \]
Next, we need to calculate \( 6^4 \):
\[ 6^4 = 6 \times 6 \times 6 \times 6 = 1296 \]
Now we can substitute this back into the equation for \( y \):
\[ y = 4.25 \times 1296 \]
Calculating this product:
\[ 4.25 \times 1296 = 5508 \]
Thus, the corresponding y-value when \( x = 4 \) is
\[ \boxed{5508} \]