Let us look at the relationship across the columns of the matrix:
* Column 1: $\text{Row }1+\text{Row }2=6+4=10$ ($\text{Row }3$)
* Column 2: $\text{Row }1+\text{Row }2=8+2=10$ ($\text{Row }3$)
* Column 3: Following the identical pattern: $\text{Row }1+\text{Row }2=7+5=12$ ($\text{Row }3$)

Thus, the missing number is $12$.