An HQ result is possible on any synth attempt, but the higher your skill level is, in comparison to the "cap" -- the skill level OF the synth itself -- the greater your chances of getting an HQ.
The conventional wisdom is that HQ chances are approximately these, for "single craftskill" items. (It varies tremendously; some times you do better, and sometimes much worse.)
Skill is 51+ over cap: 40-50% chance of HQ
Skill is 31+ over cap: 20-25%
Skill is 11+ over cap: 8-10%
Skill is 10-over-cap or less: negligible chance (but not 0%)