When working $3$ hours per day, Anvita alone can complete a piece of work in $8$ days and Maya alone can complete it in $12$ days. If they work together for $7.2$ hours per day, in how many days will they complete the work?

Let's convert total work requirement into total hours:
* Total hours required by Anvita $=8\times 3=24\text{hours}$
* Total hours required by Maya $=12\times 3=36\text{hours}$

Let total work be $\text{LCM}(24,36)=72\text{units}$.

* Efficiency of Anvita $=\frac{72}{24}=3\text{units/hour}$
* Efficiency of Maya $=\frac{72}{36}=2\text{units/hour}$
* Combined efficiency $=3+2=5\text{units/hour}$

Total hours needed working together:

$$\text{Total Hours}=\frac{72}{5}=14.4\text{hours}$$

Since they work $7.2\text{hours/day}$:

$$\text{Number of Days}=\frac{14.4}{7.2}=2\text{days}$$