The correct answer is After I took a nice hot shower, my cat lapped up the water on the floor.
Step-by-step explanation:
A dangling modifier is a term used for an ambiguous grammatical construction in which one word might be incorrectly linked to a modifier (a word that modify a noun). In the example given, in the case given the relationship between nouns and verbs is not clear as it is not clear whether it was the cat who took a hot shower and then lapped up the water or there is another subject involved. However, in the sentence "After I took a nice hot shower, my cat lapped up the water on the floor" each of the actions in the sentence (took a shower and lapped up) are linked to a subject in a clear way so there is no ambiguity in which subject carried out each action and thus the dangling modifier disappears.