To find the number of people who have watched the video after 3 days using the function \( y = 4(6)^t \), we need to substitute \( t = 3 \) into the equation:
\[ y = 4(6)^3 \]
First, calculate \( 6^3 \):
\[ 6^3 = 6 \times 6 \times 6 = 216 \]
Now, substitute this back into the equation:
\[ y = 4 \times 216 \]
Now calculate \( 4 \times 216 \):
\[ 4 \times 216 = 864 \]
Thus, the number of people who have watched the video after 3 days is \( \boxed{864} \).