Let's first express the given polynomials clearly:

The first polynomial is: $\frac{7}{8}x^2 - \frac{6}{5}x + 2$

The second polynomial is: $-2 + 4x - \frac{3}{8}x^2$

Now, let's add the polynomials:

1. Combine the $x^2$ terms: $\frac{7}{8}x^2 - \frac{3}{8}x^2 = \frac{4}{8}x^2 = \frac{1}{2}x^2$

2. Combine the $x$ terms: $-\frac{6}{5}x + 4x = -\frac{6}{5}x + \frac{20}{5}x = \frac{14}{5}x$

3. Combine the constant terms: $2 - 2 = 0$

Thus, the sum of the polynomials is: $\frac{1}{2}x^2 + \frac{14}{5}x$

Let me know if you need more details or have any questions!

Here are 5 related questions you might find interesting:

1. How do you add polynomials with different degrees?
2. What happens when the powers of $x$ in polynomials are not the same?
3. How do you handle fractions when adding polynomials?
4. What is the process of subtracting polynomials?
5. How can we factor the resulting polynomial?

Tip: When adding polynomials, always ensure you combine like terms, which are terms that have the same variable raised to the same power.