1. **State the problem:** Calculate the value of the expression $75 - 54 \div 9 \times 3 + 21$. 2. **Recall the order of operations:** Use PEMDAS/BODMAS rules: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). 3. **Perform division and multiplication first, from left to right:** - Calculate $54 \div 9 = 6$ - Then multiply $6 \times 3 = 18$ 4. **Rewrite the expression with these results:** $$75 - 18 + 21$$ 5. **Perform addition and subtraction from left to right:** - Calculate $75 - 18 = 57$ - Then add $57 + 21 = 78$ 6. **Final answer:** $$\boxed{78}$$