1. **Problem Statement:** Calculate the value of the expression $$|2 - 4 \times 6 \div 3 + \sqrt{1}|$$. 2. **Formula and Rules:** Follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). 3. **Step-by-step Calculation:** - Calculate multiplication and division first: $$4 \times 6 = 24$$ $$24 \div 3 = 8$$ - Substitute back into the expression: $$|2 - 8 + \sqrt{1}|$$ - Calculate the square root: $$\sqrt{1} = 1$$ - Simplify inside the absolute value: $$2 - 8 + 1 = (2 - 8) + 1 = -6 + 1 = -5$$ - Take the absolute value: $$|-5| = 5$$ 4. **Final Answer:** $$\boxed{5}$$