Here's how we can find the number of possible ways to assign values to A, B, C, and D:

Constraints:

A, B, C, and D are distinct integers from 0 to 9.

A + B = C

A - B = D

Solving for B:

From the second equation, we can express B as B = A - D.

Substituting B in the first equation:

A + (A - D) = C

Combine like terms: 2A - D = C

Relating C and D:We now have two equations with two unknowns (A and D). However, we can't directly solve for A or D because both equations involve them.

Instead, we can try to relate C and D. Notice that the difference between the two equations is simply D: (2A - D) - (A - D) = C - D.

This simplifies to A = C - D.

Finding possible values:

Now we have two independent equations:

A = C - D

2A - D = C

We can substitute the first equation into the second equation to eliminate A:

2(C - D) - D = C

Expand and rearrange: C - 3D = 0

Therefore, C = 3D (since C and D are distinct, D cannot be 0).

Counting possibilities:

We know that C = 3D and 0 <= C, D <= 9.

The possible values for D are 1, 3 (since C and D are distinct).

For each value of D, there are 9 possible values for C (since 0 <= C <= 9).

Therefore, there are 2 * 9 = 18 possible combinations of C and D.

Considering A and B:

For each valid combination of C and D, there is only one possible value for A (A = C - D).

The value of B is then uniquely determined by B = A - D.

Final answer:

There are 18 possible combinations of C and D, and each combination leads to a unique solution for A, B, C, and D.

Therefore, there are a total of 18 possible ways to assign values to A, B, C, and D.

So, there are 18 possible ways to assign values to A, B, C, and D.