You can't just say 'three cat'
In Mandarin you don't say 'three cat' — you say 'three [measure word] cat,' like 'three head of cattle' in English. Measure words are the little classifiers that must sit between a number and its noun.
You can't just count nouns directly
In Mandarin, a number is almost always followed by a measure word before the noun. The most common, all-purpose measure word is 个 (gè). So 'three people' is 三个人 (sān gè rén), literally 'three [measure] person'.
Number + measure word + noun
The pattern is fixed: 一个苹果 (yí gè píngguǒ) = one apple. English has a hint of this in 'two sheets of paper' — Mandarin does it for everything.
Simulation · Vocabulary flashcards
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Drill number + 个 + noun until the pattern feels natural.