Three, (20 points) For a certain project, Team A alone needs 12 days to complete, and Team B alone needs 9 days to complete. If the two teams are scheduled to work in whole days, how many schemes are there to ensure that the project is completed within 8 days?
Three, let teams A and B work for $x, y$ days respectively to just meet the requirements. Then we have
$$
\left\{\begin{array}{l}
\frac{x}{12}+\frac{y}{9}=1, \\
0 \leqslant x \leqslant 8, \\
0 \leqslant y \leqslant 8,
\end{array}\right.
$$

and $x, y$ are both integers.
From $\frac{x}{12}+\frac{y}{9}=1$, we get $x=12-y-\frac{y}{3}$.
Since $x$ and $y$ are both integers, and $0 \leqslant y \leqslant 8$, so, $y=0$ or 3 or 6.
When $y=0$, $x=12$ (discard);
When $y=3$, $x=8$;
When $y=6$, $x=4$.
Therefore, there are two solutions, one is A works for 8 days, B works for 3 days; the other is A works for 4 days, B works for 6 days.