Given the equations:

$$
\(\begin{aligned}
& (a+6)(a-6)=0 \Longrightarrow a=-6 \text { or } a=6 \\
& (b+6)(b-6)=0 \Longrightarrow b=-6 \text { or } b=6
\end{aligned}\)
$$


We need to compare:
Quantity A: $a+6$
Quantity B: $b+6$

Possible values for each quantity:
- If $a=-6$, then $a+6=0$
- If $a=6$, then $a+6=12$

Similarly for $b$ :
- If $b=-6$, then $b+6=0$
- If $b=6$, then $b+6=12$

Possible comparisons:
- If $a=-6$ and $b=6$, Quantity $\(\mathrm{A}=0\)$ and Quantity $\(\mathrm{B}=12 \rightarrow\)$ Quantity B is greater
- If $a=6$ and $b=-6$, Quantity $\(\mathrm{A}=12\)$ and Quantity $\(\mathrm{B}=0 \rightarrow\)$ Quantity A is greater
- If $a=b$, quantities are equal.

Conclusion:
The relationship cannot be determined from the information given. Each quantity can be equal or can be greater than the other depending on values of $a$ and $b$.