To determine which quadratic equations can be solved by grouping, we look for factors of the quadratic that can be grouped together.
1. **\(x^2 + 8x - 22 = 0\)**: This does not factor nicely for grouping since it does not produce simple integer factors.
2. **\(x^2 + 10x + 21 = 0\)**: This factors nicely as \((x + 3)(x + 7) = 0\). However, it can also be solved by observation without needing to group.
3. **\(x^2 - 4x - 8 = 0\)**: This does not produce factors easily and doesn’t lend itself well to grouping.
4. **\(x^2 - 12x + 18 = 0\)**: This also does not factor nicely for grouping.
In conclusion, none of these equations can specifically be classified as easily solved by grouping. However, **\(x^2 + 10x + 21 = 0\)** can be solved through factoring, but it's not the classic case of "solving by grouping."
If you’re looking for the best candidate from the list for grouping, I would say **none fit perfectly**, but the simplest form of factoring appears in **\(x^2 + 10x + 21 = 0\)**.