1. The problem asks for the cost of the flooring after a 20% discount. 2. The original cost without discount is given as $596.4. 3. To find the discount amount, use the formula: $$\text{Discount} = \text{Original Price} \times \text{Discount Rate}$$ 4. Substitute the values: $$\text{Discount} = 596.4 \times 0.20 = 119.28$$ 5. Subtract the discount from the original price to get the final price: $$\text{Final Price} = 596.4 - 119.28$$ 6. Show the cancellation step: $$\text{Final Price} = 596.4 - \cancel{119.28} + \cancel{119.28} - 119.28$$ 7. Simplify: $$\text{Final Price} = 477.12$$ 8. Therefore, the flooring will cost $477.12 after the 20% discount.