To determine how many pounds of peaches Tammy can buy along with a gallon of milk with her budget of $9.60, we start by calculating the cost of the gallon of milk:
- Cost of a gallon of milk: $3.60
Now, we subtract the cost of the milk from Tammy's total budget:
\[ \text{Remaining budget for peaches} = \text{Total budget} - \text{Cost of milk} = 9.60 - 3.60 = 6.00 \]
Next, we find out how many pounds of peaches Tammy can buy with her remaining budget of $6.00. Since peaches cost $1.20 per pound, we divide the remaining budget by the cost of peaches per pound:
\[ \text{Pounds of peaches} = \frac{\text{Remaining budget}}{\text{Cost of peaches per pound}} = \frac{6.00}{1.20} \]
Calculating this gives:
\[ \text{Pounds of peaches} = 5 \]
Therefore, Tammy can buy 5 pounds of peaches along with a gallon of milk.