A pair works only if the value you computed is $\le 12$.

The problem states $x$ and $y$ are nonnegative integers, so negative values would not be allowed (even if they satisfied the inequality).

In Desmos, enter $3x+2y\le 12$.

Enter $x\ge 0$ and $y\ge 0$ to restrict to the first quadrant.

Plot $(0,6)$, $(2,4)$, $(3,2)$, and $(4,1)$ and see which point lies in the shaded solution region. The point that lies in the region is the answer.

Evaluate $3x+2y$ for each point:

• $(0,6)$: $3(0)+2(6)=12$
• $(2,4)$: $3(2)+2(4)=14$
• $(3,2)$: $3(3)+2(2)=13$
• $(4,1)$: $3(4)+2(1)=14$

The constraint requires $3x+2y\le 12$. Only $(0,6)$ gives $12$, which is allowed.

Therefore, the correct answer is $(0, 6)$.