Which set of side lengths could NOT form a triangle?

The triangle inequality says that the sum of any two sides must be greater than the third side. For $4, 7, 12$: $4+7=11$, which is not greater than $12$, so these lengths cannot form a triangle, choice G. The other sets all pass: $5+6>7$ for choice F; $8+8>8$ for choice H; $6+8>10$ for choice J (a right triangle, since $36+64=100$). It is enough to test the two shorter sides against the longest side. If their sum is equal to or less than the longest side, the shorter sides cannot meet.