"You like very many fish."
Translation:Plurimi pisces tibi placent.
plurimi here is nominative plural case (nominative case being the subject of the sentence, the one 'doing' the 'verb').
plurimos would be the accusative plural case (the accusative is often the direct object, the one the 'verb' is 'performed' upon).
Since, plurimi is an adjective it has to agree in case with the noun it modifies. Here, pisces.
It is unlikely to be fishes, not because it is wrong, but because it is not the normally used plural, though it would depend on context. In English, fish is both singular and plural. Hence, we would say "there are many fish in the sea" or "there are many types of fish in the sea" or "I don't like eating fish dishes". Nevertheless, one can use fishes as the plural, but it is much more rare to do so and tends to be used mostly when one wants to subtly emphasise the plurality, perhaps to make the sentence more artistically effective. This is a rather vague explanation, but I hope it helps a bit.
If you are not a native English speaker, my advice is to avoid using fishes and stick with fish as both singular and plural. When listening, you should be able to work out which someone means from the rest of the sentence, but also don't worry if you hear someone using fishes.
In american english, we only use 'fishes' when referring to the various breeds of fish... like if you pulled a net out of the water and had catfish, snapper, and gar. And even that use is rare.
But when referring to quantity, fish is both singular and plural.
The same for food and foods.
The confusion comes about because the English translation is a 'natural' translation, not a literal translation. In the sentence, 'You like very many fish' the subject is 'you' and 'very many fish' would be the object. In the Latin, not that tibi is in the dative case and therefore translates as 'to/for you'. The more literal translation is therefore, 'Very many fish are pleasing to/for you.' It is easy to see here that 'very many fish' is the subject (therefore nominative case) because it answers the question, 'Who or what was doing the pleasing?'