1. Stating the problem: Simplify the expression $$3 \left(\frac{11}{12} - \frac{5}{6}\right) + \frac{3}{4}$$. 2. Use the order of operations: first simplify inside the parentheses, then multiply, and finally add. 3. Find a common denominator for the fractions inside the parentheses: $$\frac{11}{12} - \frac{5}{6} = \frac{11}{12} - \frac{10}{12} = \frac{11 - 10}{12} = \frac{1}{12}$$. 4. Multiply the result by 3: $$3 \times \frac{1}{12} = \frac{3}{12} = \frac{\cancel{3}}{\cancel{12}} = \frac{1}{4}$$. 5. Add $$\frac{1}{4} + \frac{3}{4} = \frac{1 + 3}{4} = \frac{4}{4} = 1$$. Final answer: $$1$$.