To add the given expressions, we will combine like terms.
### Expression 1:
\[
-3k + 4k^3 - 2 - 3k + 4k^3 - 2
\]
1. Combine the \( k^3 \) terms:
\[
4k^3 + 4k^3 = 8k^3
\]
2. Combine the \( k \) terms:
\[
-3k - 3k = -6k
\]
3. Combine the constant terms:
\[
-2 - 2 = -4
\]
So, Expression 1 simplifies to:
\[
8k^3 - 6k - 4
\]
### Expression 2:
\[
9k^2 - 3k^3 + 4k - 39k^2 - 3k^3 + 4k - 3
\]
1. Combine the \( k^3 \) terms:
\[
-3k^3 - 3k^3 = -6k^3
\]
2. Combine the \( k^2 \) terms:
\[
9k^2 - 39k^2 = -30k^2
\]
3. Combine the \( k \) terms:
\[
4k + 4k = 8k
\]
4. Combine the constant terms:
\[
-3
\]
So, Expression 2 simplifies to:
\[
-6k^3 - 30k^2 + 8k - 3
\]
### Final Step: Adding Expression 1 and Expression 2
Now, combine the two simplified expressions:
\[
(8k^3 - 6k - 4) + (-6k^3 - 30k^2 + 8k - 3)
\]
1. Combine the \( k^3 \) terms:
\[
8k^3 - 6k^3 = 2k^3
\]
2. Combine the \( k^2 \) terms:
\[
0k^2 - 30k^2 = -30k^2
\]
3. Combine the \( k \) terms:
\[
-6k + 8k = 2k
\]
4. Combine the constants:
\[
-4 - 3 = -7
\]
So, the final result, after combining both expressions, is:
\[
\boxed{2k^3 - 30k^2 + 2k - 7}
\]