Technically, there is no specific answer to your problem. That is because you have 5 variables and only 4 equations. is not now, never has been, and never will be the same thing as . However, presuming that you were simply being sloppy...
a + b = 8 => a = 8 - b
b + d = 8 => d = 8 - b, so the first thing we know is that a = d

a + c = 13 => a = 13 - c
c - d = 6 => d = c - 6
but since a = d
c - 6 = 13 - c => 2c = 19 => c = 9.5.

**Quize: A B=6, A C=13, B D=8, C-D=6? Explain in detail.**

To solve this quize, we need to carefully analyze the given equations and determine the values of A, B, C, and D. Let's break down the problem step by step:

**Step 1: Analyzing the given equations:**

We are given the following equations:
1. A B = 6
2. A C = 13
3. B D = 8
4. C - D = 6

We need to find the values of A, B, C, and D that satisfy these equations.

**Step 2: Solving the equations:**

Let's start by solving the first equation, A B = 6. Since we don't have any other information about A or B, we can't determine their specific values. However, we can find the possible combinations of A and B that multiply to 6. The factors of 6 are (1, 6) and (2, 3). So, A and B can have the values of 1 and 6 or 2 and 3.

Moving on to the second equation, A C = 13. We already found the possible values of A (1 or 2). Now, we can substitute these values and find the corresponding values of C. If A = 1, then C = 13/1 = 13. If A = 2, then C = 13/2 = 6.5. However, since we are not allowed to have decimal values, we can only consider the case where A = 1 and C = 13.

Next, let's consider the third equation, B D = 8. We already found the possible values of B (6 or 3). Now, we can substitute these values and find the corresponding values of D. If B = 6, then D = 8/6 = 1.33 (rounded to two decimal places). Since we are not allowed to have decimal values, we can only consider the case where B = 3 and D = 8/3 = 2.67 (rounded to two decimal places).

Finally, let's examine the fourth equation, C - D = 6. We found that C = 13 and D = 2.67. Substituting these values into the equation, we get 13 - 2.67 = 10.33. However, since we are not allowed to have decimal values, the equation C - D = 6 is not satisfied by the values we found.

**Step 3: Conclusion:**

After careful analysis, we have determined that there are no values of A, B, C, and D that satisfy all the given equations simultaneously. Therefore, the given set of equations is inconsistent, and it is not possible to find a solution.

Note: It is important to always thoroughly analyze the given equations and consider any restrictions or limitations in order to find a valid solution.