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To determine how many ounces of water need to be added to dilute a solution from a higher concentration to a lower concentration, it is essential to understand the principle of dilution and how concentrations work.

The initial solution contains 24 ounces of a liquid that is 44% alcohol. This means that the actual amount of alcohol in the solution is calculated as follows:

Amount of alcohol = 24 ounces x 0.44 = 10.56 ounces of alcohol.

Next, we want to dilute this solution so that the final concentration of alcohol is 20%. Let the amount of water that needs to be added be represented as \( x \) ounces. After adding water, the total volume of the new solution will be:

Total volume = 24 ounces + \( x \) ounces.

We want the alcohol to now comprise 20% of this new total solution. Therefore, we can set up the following equation for the desired concentration:

10.56 ounces of alcohol = 20% of (24 ounces + \( x \) ounces).

This can be written mathematically as:

10.56 = 0.20(24 + \( x \)).

Expanding this gives:

10.56 = 4.8 + 0.20