Lindsey is considering purchasing an item that costs $\$ 1200$ and has a discount of $20 \%$. What is the amount of discount on the item? Round your answer to the nearest cent, if necessary.

Step 1 ：Lindsey is considering purchasing an item that costs $1200 and has a discount of 20%. We need to find the amount of discount on the item.

Step 2 ：The amount of discount on the item can be calculated by multiplying the cost of the item by the discount rate.

Step 3 ：In this case, the cost of the item is $1200 and the discount rate is 20% or 0.20 when expressed as a decimal.

Step 4 ：Let's denote the cost of the item as \(cost_{item}\) and the discount rate as \(discount_{rate}\). So, \(cost_{item} = 1200\) and \(discount_{rate} = 0.2\).

Step 5 ：The discount amount can be calculated using the formula: \(discount_{amount} = cost_{item} \times discount_{rate}\).

Step 6 ：Substituting the given values into the formula, we get \(discount_{amount} = 1200 \times 0.2 = 240.0\).

Step 7 ：Final Answer: The amount of discount on the item is \(\boxed{240}\) dollars.