To find the area of the frame, we need to subtract the area of the square hole from the area of the entire cardboard.

Step-by-step:

1. Area of the entire cardboard:
   The cardboard is a square with sides of 12 inches.
   $\text{Area of cardboard} = 12^2 = 144 \, \text{square inches}$

2. Area of the square hole:
   The hole is also a square with sides of length $s$.
   $\text{Area of hole} = s^2$

3. Area of the frame:
   To find the area of the frame, subtract the area of the hole from the area of the cardboard:
   $\text{Area of frame} = 144 - s^2$

Now, looking at the answer choices, the correct expression is:

$\boxed{12^2 - s^2}$

Would you like me to explain any part of this further?

Related Questions:

1. How would the expression change if the cardboard was 15 inches on each side?
2. What happens to the frame's area as $s$ gets closer to 12 inches?
3. How would you express the area if the hole was a circle instead of a square?
4. What if the cardboard was rectangular instead of square?
5. How do you expand $(12 - s)^2$ to compare it with the other expressions?

Tip:

When dealing with area problems, always identify the shapes involved and remember to subtract the "missing" part if there's a hole or cut-out!