Add the expressions.

To add the given expressions, we first align the terms based on their degree:

### Expression 1:
\(-3k + 4k^3 - 2\)

### Expression 2:
\(9k^2 - 3k^3 + 4k - 3\)

Now, let's identify their terms:

- **Cubic terms**: \(4k^3\) from Expression 1 and \(-3k^3\) from Expression 2.

- **Quadratic terms**: \(9k^2\) from Expression 2 (no quadratic term in Expression 1).

- **Linear terms**: \(-3k\) from Expression 1 and \(4k\) from Expression 2.

- **Constant terms**: \(-2\) from Expression 1 and \(-3\) from Expression 2.

Now, we can add the matching terms:

1. **Cubic terms**:
\(4k^3 - 3k^3 = (4 - 3)k^3 = 1k^3 = k^3\)

2. **Quadratic terms**:
\(0 + 9k^2 = 9k^2\)

3. **Linear terms**:
\(-3k + 4k = (4 - 3)k = 1k = k\)

4. **Constant terms**:
\(-2 - 3 = -5\)

### Final combined expression:

Putting all of this together, we get:

\[
k^3 + 9k^2 + k - 5
\]

Thus, the result of adding the two expressions is:

\[
k^3 + 9k^2 + k - 5
\]