Correct spelling, explanation: nineteen is a combination of the word nine and suffix -teen. Words ending with e behave with suffixes in two different ways: we drop the e if the suffix begins with a vowel (for example -ing, -ity) and we don’t drop the e if the suffix begins with a consonant. The suffix -teen begins with a consonant, so nineteen is the correct spelling and ninteen is incorrect.

Definition of nineteen:
numeral, the cardinal number between eighteen and twenty
He failed the test dramatically. He got only nineteen percent.
I didn’t buy the book, because it was nineteen pounds. What a rip-off!

Incorrect spelling, explanation: suffix -teen begins with a consonant, which means we do not omit the final vowel e in the word we combine it with. Therefore nineteen should be spelled with e in the middle. If a suffix begins with a vowel, then we skip the e from the end of the word. Here however it’s not the case and ninteen is incorrect.