The trick in this question is hidden in the word hydantoin. Phenytoin is chemically a hydantoin derivative, so any syndrome named fetal hydantoin syndrome must come from phenytoin exposure in the womb. The link is built into the terminology itself.
Babies affected by this syndrome show a recognizable cluster: an unusual facial shape, underdeveloped tips of the fingers with small nails, slowed growth, a small head, learning difficulties, and occasionally a cleft lip or palate. These effects are thought to arise from reactive epoxide breakdown products of phenytoin damaging fetal tissue.
The other antiepileptics cause their own distinct problems. Valproate and carbamazepine are both tied to neural tube defects such as spina bifida, and phenobarbitone has a broad teratogenic risk, but none of them carry the hydantoin name. Phenytoin is the cause.
\[\boxed{\text{Phenytoin}}\]