Answer :

Certainly! Let's discuss and find the inverse operations for each given scenario step-by-step.

### 1. Add 12
For the first operation, the task is to state the inverse operation of "Add 12".

#### Step-by-Step Solution:
1. The original operation is adding 12 to a number.
2. To negate the effect of adding 12, we need an operation that will bring the number back to its original state.
3. The inverse of addition is subtraction.

Therefore, the inverse operation of "Add 12" is:
- Subtract 12

### 4. Subtract -15
For the fourth operation, the task is to state the inverse operation of "Subtract -15".

#### Step-by-Step Solution:
1. The original operation is subtracting -15 from a number.
2. Subtracting a negative number is equivalent to adding the positive counterpart of that number. Thus, subtracting -15 is the same as adding 15.
3. To negate the effect of subtracting -15, we need an operation that will bring the number back to its original state.
4. The inverse of subtracting a negative number (or adding its positive counterpart) is subtracting the positive counterpart.

Therefore, the inverse operation of "Subtract -15" is:
- Add 15

### Summary:
- The inverse operation of "Add 12" is "Subtract 12".
- The inverse operation of "Subtract -15" is "Add 15".

Please let me know if you have any questions or if there's anything else you'd like to discuss!