Korean · Pronunciation Guide
net -- dental n, the vowel of 'bed', and a final t that closes without releasing.
net
One clipped beat. The practical concern is the pairing with 셋: both are single syllables, both end in the same neutralized stop, and both use the same vowel, so the entire contrast rests on the first consonant.
Listen: 넷
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우리 가족은 넷이에요.
Uri gajogeun nesieyo.
There are four in my family.
Listen: 우리 가족은 넷이에요.
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우리 가족은 넷이에요 revives the hidden ㅅ -- attached to 이에요 the word becomes ne-si-e-yo with a clear s opening the next syllable. Listen for that and you will understand why Korean spells the word with ㅅ despite never pronouncing one in isolation.
The historical distinction between ㅐ and ㅔ has largely collapsed for younger Seoul speakers, so do not agonize over the vowel quality. The real error is releasing the final consonant with an audible English t-burst, or adding a small vowel after it and saying 'net-uh', either of which turns a one-syllable numeral into two.