1. **State the problem:** Simplify the expression $10 + \left(\frac{27}{3} \times 12\right) - 6 \times 4$ and express the result as a fraction in lowest terms. 2. **Recall order of operations:** Perform operations inside parentheses first, then multiplication and division from left to right, and finally addition and subtraction. 3. **Calculate inside the parentheses:** $$\frac{27}{3} = 9$$ So the expression becomes: $$10 + (9 \times 12) - 6 \times 4$$ 4. **Multiply inside the parentheses:** $$9 \times 12 = 108$$ Expression now: $$10 + 108 - 6 \times 4$$ 5. **Multiply the last term:** $$6 \times 4 = 24$$ Expression now: $$10 + 108 - 24$$ 6. **Perform addition and subtraction from left to right:** $$10 + 108 = 118$$ Then: $$118 - 24 = 94$$ 7. **Express as a fraction in lowest terms:** $$94 = \frac{94}{1}$$ Since 94 and 1 have no common factors other than 1, the fraction is already in lowest terms. **Final answer:** $$\boxed{\frac{94}{1}}$$