Simplify the following expression.

$(6+\mathrm{6 }\text{of }5÷5)÷6\text{ of}\mathrm{ 5}+(24÷2\text{ of }3-6\text{ of}\mathrm{ 5}+4)$

The correct answer is Option 2: $-21\frac{3}{5}$.

We need to simplify:

$(6+6\text{of}5÷5)÷6\text{of}5+(24÷2\text{of}3-6\text{of}5+4)$

We follow the BODMAS rule. The keyword "of" means multiplication and is applied before Division (÷) in the order of operations. Let us work through this in two parts.

Part 1: Simplify the first bracket and its division

Focus on: $(6+6\text{of}5÷5)÷6\text{of}5$

Step 1: Inside the bracket, handle "of" first:
6 of 5 = 6 × 5 = 30

Step 2: Inside the bracket, now do the division:
30 ÷ 5 = 6

Step 3: Complete the bracket addition:
6 + 6 = 12

Step 4: Now handle "6 of 5" outside the bracket (this is the divisor):
6 of 5 = 6 × 5 = 30

Step 5: Divide the bracket result by 30:
12 ÷ 30 = $\frac{12}{30}=\frac{2}{5}$

Part 2: Simplify the second bracket

Focus on: $(24÷2\text{of}3-6\text{of}5+4)$

Step 6: Handle all "of" operations first:
2 of 3 = 2 × 3 = 6
6 of 5 = 6 × 5 = 30

Step 7: Now do the division:
24 ÷ 6 = 4

Step 8: The bracket becomes:
4 - 30 + 4 = 8 - 30 = -22

Final Step: Combine both parts

$\frac{2}{5}+(-22)=\frac{2}{5}-22$

Converting to a mixed number:

$\frac{2}{5}-\frac{110}{5}=\frac{2-110}{5}=\frac{-108}{5}=-21\frac{3}{5}$

Therefore, the simplified value of the expression is:

$-21\frac{3}{5}$