If $A$ is of order $2\times 3$ and $B$ is of order $3\times 4$, then the product $AB$ is defined and has order

Matrix multiplication is possible when the number of columns of the first matrix equals the number of rows of the second. Here, $A$ is $2\times 3$ and $B$ is $3\times 4$, so $AB$ exists and has order given by the outer numbers: $2\times 4$.