Is $3 \times 2 = 3+3$ or $2+2+2$? $3\times 2$ is $3+3$ or $2+2+2$. We know both are correct as multiplication is commutative for whole numbers. But which one is mathematically accurate?

In every ring and even in every semiring, $3 \times 2$ is by definition $(1+1+1)\times (1+1)$ . Since multiplication distributes over addition, you get on the one hand
$$
(1+1+1) \times (1+1) = (1+1+1) + (1+1+1) = 3 +3
$$
and on the other hand
$$
(1+1+1) \times (1+1) = (1+1) + (1+1) + (1+1) = 2 + 2 + 2
$$
