Final answer:
The non-permissible replacement for 'a' in the expression a^2/3a+6 is -2.
Step-by-step explanation:
To find the non-permissible replacement for a in the expression a^2/3a+6, we need to determine the values of a that would result in an undefined or non-permissible value. In this case, the non-permissible replacement for a occurs when the denominator is equal to zero. So, we need to solve the equation 3a+6=0 to find the value of a that makes the expression undefined.
Solving the equation 3a+6=0 gives us a=-2. Therefore, the non-permissible replacement for a is -2.