Raksha can complete a piece of work in $12\text{ days}$ while Esther takes $20\text{ days}$ to complete the work. They start working together but Raksha leaves $4\text{ days}$ before the work gets over. For how many days does Esther work?

Let the total work be the $\text{LCM}$ of $12$ and $20$.
$$\text{Total Work}=\text{LCM}(12,20)=60\text{ units}$$

Now, find their individual efficiencies:

$$\text{Efficiency of Raksha}=\frac{60}{12}=5\text{ units/day}$$

$$\text{Efficiency of Esther}=\frac{60}{20}=3\text{ units/day}$$

Let the total number of days the work lasted be $x$.
Since Esther worked for all $x$ days and Raksha left $4$ days before completion, Raksha worked for $(x-4)$ days.

The total work equation is:

$$\text{Work done by Raksha}+\text{Work done by Esther}=\text{Total Work}$$

$$5(x-4)+3x=60$$

$$5x-20+3x=60$$

$$8x=80$$

$$x=10\text{ days}$$

Since Esther worked for the entire duration, Esther worked for $10$ days.