1. Stating the problem: Evaluate the expression $$42. |120| - |-45|$$. 2. Recall that the absolute value of a number is its distance from zero on the number line, always non-negative. So, $$|120| = 120$$ and $$|-45| = 45$$. 3. Substitute these values into the expression: $$42. \times 120 - 45$$ 4. Perform the multiplication: $$42. \times 120 = 5040$$ 5. Now subtract: $$5040 - 45 = 4995$$ 6. Final answer: $$\boxed{4995}$$