게 알리다

let someone know, kindly or otherwise

알려주다 is the everyday verb for both telling someone something and teaching them, and -게 supplies the manner. 친절하게 알려주다 "explain it kindly" fills four of these lines, mostly inside thank-yous: 친절하게 알려 주셔서 정말 고맙습니다. 이렇게 알려주다 "explain it like this" is the demonstrating use. Note that 주다 is almost always attached — bare 알리다 sounds like an official announcement.