Add the expressions.

To add the two expressions, we will combine like terms.

Expression 1: \( -3k + 4k^3 - 2 \)
Expression 2: \( 9k^2 - 3k^3 + 4k - 3 \)

Now let's rewrite the expressions:

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

2. For \( k^2 \) terms:
\( 0 + 9k^2 = 9k^2 \) (since there are no \( k^2 \) terms in Expression 1)

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

4. For constant terms:
\( -2 - 3 = -5 \)

Now combine these results:

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

Therefore, the final result of adding the two expressions is:

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