To find out how many gallons of blue paint must be used, we first need to determine the total parts of the mixed paint. The mix ratio is 3 parts yellow to 2 parts blue.
We can calculate the total parts as follows: \[ \text{Total parts} = 3 , (\text{yellow}) + 2 , (\text{blue}) = 5 , \text{parts} \]
Now, we know that we need 12 gallons of mixed paint. To find the volume of each part, we can divide the total volume by the total parts: \[ \text{Volume per part} = \frac{12 , \text{gallons}}{5 , \text{parts}} = 2.4 , \text{gallons per part} \]
Next, we need to find out how many gallons of blue paint are required. Since blue is 2 parts of the total 5 parts, we can calculate the amount of blue paint as follows: \[ \text{Gallons of blue} = 2 , \text{parts (blue)} \times 2.4 , \text{gallons per part} = 4.8 , \text{gallons} \]
Therefore, the amount of blue paint required is \( \boxed{4.8} \) gallons.