Oh come on, it was so obvious! There was no chemistry between you two! You definitely shouldn’t call that girl with the braided hair!
編む is "to knit." When you knit in threes, you are knitting in a braid style. What do you braid? Hair. That makes this braided hair.
The reading is the み from 三つ and つ and 編む combined into one (or should I say three?) braids. Just watch out because this isn't みっつあみ, it's just みつあみ. Listen to the audio a few times to make sure you remember how it's spelled and pronounced!