The average of six numbers is $12$. The average of two of them is $6.5$, while the average of the other two is $4.5$. What is the average of the remaining two numbers?

Total sum of all $6$ numbers:
$$\text{Total Sum}=6\times 12=72$$

Sum of the first two numbers:

$${\text{Sum}}_1=2\times 6.5=13$$

Sum of the next two numbers:

$${\text{Sum}}_2=2\times 4.5=9$$

Sum of these four numbers:

$$\text{Sum of 4 numbers}=13+9=22$$

Sum of the remaining two numbers:

$$\text{Remaining Sum}=72-22=50$$

Average of the remaining two numbers:

$$\text{Average}=\frac{50}{2}=25$$