黙っといて... What is this form?
黙っといての「っと」は何ですか？
What is "tto" in "damattoite"?
¿Qué es "tto" en "damattoite"?
そして、何で「黙っといて」はて形にある？
Also, why "damattoite" is in Te form?
Además, ¿por qué "damattoite" está en Forma Te?
Thanks! ありがとう！Gracias!Ignore the above detail thanks (:Thanks! (:Please Ignore "Ignore the above detail" (I don't know how edit this stupid questions D: )

Question

黙っといて... What is this form?
黙っといての「っと」は何ですか？
What is "tto" in "damattoite"?
¿Qué es "tto" en "damattoite"?
そして、何で「黙っといて」はて形にある？
Also, why "damattoite" is in Te form?
Además, ¿por qué "damattoite" está en Forma Te?
Thanks! ありがとう！Gracias!Ignore the above detail thanks (:Thanks! (:Please Ignore "Ignore the above detail" (I don't know how edit this stupid questions D: )

Answer

I suggest you look up the verb 黙る and the verb おく(used as a subsidiary verb here; "the te-form verb + おく"

Answer

「黙っといて」 is the short form of 「黙っておいて」 and is mostly used in speaking.
So, the 「てお」 is simply replaced by 「と」 when you speak.
Also I believe if you speak 「黙っておいて」 quick enough, it will sound like 「黙っといて」. May be that is where it came from.