1. **State the problem:** Simplify the expression $$6 \div 2 - \left(81 \div 3^2\right)$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)). 3. **Evaluate the exponent:** Calculate $$3^2 = 9$$. 4. **Simplify inside the parentheses:** $$81 \div 9 = 9$$. 5. **Rewrite the expression:** $$6 \div 2 - 9$$. 6. **Perform division:** $$6 \div 2 = 3$$. 7. **Substitute back:** $$3 - 9$$. 8. **Perform subtraction:** $$3 - 9 = -6$$. **Final answer:** $$-6$$.