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To solve the inequality \( x + 6 > -2 \), we can start by isolating \( x \).
1. Subtract 6 from both sides:
\[
x + 6 - 6 > -2 - 6
\]
\[
x > -8
\]
Now, we have the solution \( x > -8 \).
The problem states that we need to find the solution set among the given options:
1. \( x | x > -8 \)
2. The solution set is null.
3. \( \{3, -8\} \)
4. \( x | x > 3 \)
Since we found that \( x > -8 \), this means that the set of possible solutions includes all numbers greater than -8.
The correct representation of this solution set would be:
- \( x | x > -8 \), which perfectly matches the first option.
Thus, the answer is:
\( x | x > -8 \)