Explanation:
To find the common difference of an arithmetic progression (AP) where the 7th term is twice the 3rd term, and the first term is 12, follow these steps:

1. Recall the formula for the \(n\)-th term of an AP:

\[
a_n = a + (n - 1) \cdot d
\]

where \(a\) is the first term and \(d\) is the common difference.

2. Write the expressions for the 7th term and the 3rd term:

- The 7th term (\(a_7\)) is:
\[
a_7 = a + 6d
\]

- The 3rd term (\(a_3\)) is:
\[
a_3 = a + 2d
\]

3. According to the problem, the 7th term is twice the 3rd term:

\[
a + 6d = 2(a + 2d)
\]

4. Substitute the first term \(a = 12\) into the equation:

\[
12 + 6d = 2(12 + 2d)
\]

5. Expand and simplify:

\[
12 + 6d = 24 + 4d
\]
\[
6d - 4d = 24 - 12
\]
\[
2d = 12
\]
\[
d = \frac{12}{2} = 6
\]

Thus, the common difference \(d\) is 6, which corresponds to option A.