Homo is third declension masculine, hominum is plural genitive ("of men"). Here you need accusative, so ad hominem.
Case Singular Plural
Nominative homō hominēs
Genitive hominis hominum
Dative hominī hominibus
Accusative hominem hominēs
Ablative homine hominibus
Vocative homō hominēs
From a French education, I have learned a different order of cases for Latin declension tables (NVAGDA: Nominative, Vocative, Accusative, Genitive, Dative, Ablative). I was curious to know where it comes from, and apparently the order you used is more common in the US: https://en.wikipedia.org/wiki/Latin_declension#Order_of_the_...
