Explanation:

- Let's define the work rates:

- Let $B$ be the work rate of one boy.

- Let $G$ be the work rate of one girl.

- From the problem:

- $4B+6G$ (work for 10 days) = 1 complete work.

- $12B+8G$ (work for 4 days) = 1 complete work.

- Set up equations based on above:

- $10(4B+6G)=1$

- $4(12B+8G)=1$

- Solve the system of equations to find $B$ and $G$.

- Calculate combined work rate for 20 boys and 30 girls:

- Work rate = $20B+30G$

- Compute time for full work:

- Total work / Total work rate = Time taken

- After calculations, you'll find it takes 2 days for 20 boys and 30 girls.

So, the correct answer is:

- Option 1: 2 days