Add the expressions.

To add the two expressions, we need to combine like terms from both expressions.

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

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

Now, we can rewrite the addition of these expressions:

\[
(-3k + 4k^3 - 2) + (9k^2 - 3k^3 + 4k - 3)
\]

Next, we can rearrange and group the like terms (by degree):

\[
(4k^3 - 3k^3) + (9k^2) + (-3k + 4k) + (-2 - 3)
\]

Now, we simplify each group:

1. For \(k^3\) terms: \(4k^3 - 3k^3 = 1k^3\) or simply \(k^3\)
2. For \(k^2\) terms: \(9k^2\) (remains the same)
3. For \(k\) terms: \(-3k + 4k = 1k\) or simply \(k\)
4. For the constant terms: \(-2 - 3 = -5\)

Now we combine the simplified terms:

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

So, the sum of the two expressions is:

\[
\boxed{k^3 + 9k^2 + k - 5}
\]