To find the value of the expression given in the question, we need to apply the BODMAS/PEMDAS rules, which stand for Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). The expression is:
\(4 \text{ of } 6 \div 3 \times 2 \frac{1}{4} + 5 \times 6 \div 15 - 3 \text{ of } 2 \times 4 \text{ of } 8 \div 32\)

Let's solve it step by step:

1. Calculate "of" and Multiplications/Divisions:
   \(4 \text{ of } 6\) means \(4 \times 6\) = \(24\).
   \(2 \frac{1}{4}\) is converted to an improper fraction = \(\frac{9}{4}\).
   \(5 \times 6 = 30\).
   \(3 \text{ of } 2 = 3 \times 2 = 6\).
   \(4 \text{ of } 8 = 4 \times 8 = 32\).
    
2. Simplify Division and Multiplication:
   \(24 \div 3 = 8\).
   \(8 \times \frac{9}{4} = \frac{72}{4} = 18\).
   \(30 \div 15 = 2\).
   \(6 \times 32 \div 32 = 6\) (since dividing and multiplying by 32 cancels out).
3. Combine the Results:
   The expression now becomes: \(18 + 2 - 6\).
4. Final Calculation:
   Solve the addition and subtraction: \(18 + 2 = 20\), then \(20 - 6 = 14\).

The value of the entire expression is 14.

Therefore, the correct answer is:

14