My niece had unprotected sex on 12/18 (6 days before her period). she started on 12/24, could she be pregnant?

Unlikely: It is unlikely but not impossible that she could be pregnant and have a normal period that starts on time. Pregnancy is always a possibility if you have unprotected intercourse.

Yes: Pregnancy from exposure on any day of a woman's cycle, including during menses, has been documented. However, those with irregular intervals/cycles would be the ones most at risk. Those with predictable patterns are less so. Pregnancy requires a fertile egg become available to a fertile sperm.