For the same reason why in English 12 = twelve, but 14 = fourteen. Not all numerals are formed by the same rule.

The correspondents of the -teen numbers in Greek were formed similarly with English, after the model of 14 = four and ten = "tetrakaideka".

"Tetrakaideka" is a contracted form of 14, normally used in compound words. When "14" was an isolated word, it would have been "tettarakaideka" or "tessarakaideka". These are the forms for the neuter gender, the numeral "4" = "tettara" or "tessara" (depending on the dialect) was changed by declension for other genders and cases.

In Ancient Greek numbers bigger than 20, the word "and" = "kai" was usually omitted, but then the bigger number was always the first like in "twenty-four". When "and" was inserted, then the order could also be inverse, like in "four-and-twenty".

kai means "and"

I guess like asking why 120 is said "one hundred and twenty" in some dialects.

Maybe that's how 14 and 12 are written in Greek.

As the sibling comment already said "kai" (pronounced ke like in keg) just means "and". So it literally means 4 and 10 sides in greek. But I have often seen it written as τετραδεκάεδρο (tetradecahedron) in greek as well, so without the kai part. I'm not sure why it is 4 and 10 instead of 14 though. It would be more natural in greek that way (δεκατετράεδρο - decatetrahedron). Maybe it is for putting the distinctive part (4) first, or maybe it sounded more "poetic" like that to someone and then it stuck.

Because the Greek word for 12 is something like "though-theka". And the word for 14 is "theka-tessera". Like most European languages, 11 and 12 are special, then it reverts to the "single digit - ten" or "ten - single digit" pattern.

"kai" is "and" in Greek.