Of the three numbers, the second is twice the first and thrice the third. If the average of the three numbers is $44$, the largest number is:

Let the second number be $6x$ (a common multiple of 2 and 3).
* The first number is half of the second $⟹3x$.
* The third number is one-third of the second $⟹2x$.

Given that the average of the three numbers is $44$:

$$\frac{3x+6x+2x}{3}=44$$

$$\frac{11x}{3}=44$$

$$11x=132⟹x=12$$

The largest number among them is the second number ($6x$):

$$\text{Largest Number}=6\times 12=72$$