**Solution:**

Let's assume that the first term of the first AP is 'a' and the common difference is 'd'. Therefore, the first AP can be represented as:

First AP: a, a + d, a + 2d, a + 3d, ...

Similarly, let's assume that the first term of the second AP is 'b' and the common difference is 'e'. Therefore, the second AP can be represented as:

Second AP: b, b + e, b + 2e, b + 3e, ...

**Finding the Sum of n Terms of the First AP:**

The sum of the first n terms of an AP is given by the formula:

S(n) = n/2 * [2a + (n-1)d]

For the first AP, the sum of n terms can be written as:

S1(n) = n/2 * [2a + (n-1)d]

**Finding the Sum of n Terms of the Second AP:**

Similarly, for the second AP, the sum of n terms can be written as:

S2(n) = n/2 * [2b + (n-1)e]

**Given Ratio of the Sum of n Terms:**

The given ratio of the sum of n terms is (3n + 4) : (5n + 6).

Therefore, we can write the ratio as:

(3n + 4) : (5n + 6) = [S1(n)] : [S2(n)]

**Finding the Ratio of the 7th Terms:**

To find the ratio of the 7th terms, we substitute n = 7 in the ratio equation.

(3(7) + 4) : (5(7) + 6) = [S1(7)] : [S2(7)]

Simplifying the equation, we get:

25 : 41 = [S1(7)] : [S2(7)]

**Explanation of the Solution:**

In this solution, we have assumed the first term and common difference of the two APs. We have then used the formula for the sum of the first n terms of an AP to find the sum of n terms for both APs. By equating the ratio of the sums of n terms to the given ratio, we can find the ratio of the 7th terms of the two APs.

It is important to note that the solution can be generalized for any values of a, d, b, and e. The given ratio of the sum of n terms can be used to find the ratio of any term in the two APs by substituting the desired value of n in the ratio equation.