Is $$x \lt 0$$?
>(1) $$y+x<0$$
>(2) $$y \gt 12$$

Correct.
The issue here is positive vs. negative.
In Statement (1), plug in a positive value for $$x$$ that satisfies the statement, then answer the question with a "No." Now plug in a negative value for $$x$$ to get a "Yes" answer. Getting "Yes" and "No" means "Maybe," so **(1) Maybe → Insufficient → BCE**.
Statement (2) is interesting but alone does not influence the value of $$x$$, so **(2) Maybe → Insufficient → CE**.
Combining both statements gives you $$y+x<0$$ where $$y$$ is larger than 12. Now $$x$$ has to be negative in order to make the left side smaller than zero. Answer the question with a definite "Yes." **(1)+(2) Yes → Sufficient → C**.

Incorrect.

Since you have no knowledge of $$y$$, it can be anything, and so can $$x$$.

Incorrect.

Statement (2) alone does not tell you anything about $$x$$.

Incorrect.

Incorrect.

Plug in numbers to support your answer.

Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient to answer the question asked.

Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient to answer the question asked.

BOTH Statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

EACH statement ALONE is sufficient to answer the question asked.

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.