To find the value of \( A(8) \) using the equation \( A(t) = 6(2)^{0.25t} \), we will substitute \( t = 8 \) into the equation.
Start with the equation: \[ A(t) = 6(2)^{0.25t} \]
Substituting \( t = 8 \): \[ A(8) = 6(2)^{0.25 \cdot 8} \]
Calculating \( 0.25 \cdot 8 \): \[ 0.25 \cdot 8 = 2 \]
Now, substitute this back into the equation: \[ A(8) = 6(2)^{2} \]
Calculating \( (2)^{2} \): \[ (2)^{2} = 4 \]
Now, multiply by 6: \[ A(8) = 6 \cdot 4 = 24 \]
Therefore, the number of bugs after 8 days is \( \boxed{24} \).