What is the meaning of -게_하다?

A propositive verb-final suffix in the "intimate" ᄒᆞ여체 (hawyeoche) speech level used between friends, by superiors to inferiors, etc.

An evidential verb-final suffix in the "intimate" ᄒᆞ여체 (hawyeoche) speech level that marks an event of which the speaker has knowledge, either from inference or observation. Only used with the -언 (-eon) and -은 (-eun) suffixes and their allomorphs.

-ly; a suffix attached to the stems of verbs and adjectives to derive adverbs.

so that

In the intimate style:

1. are you going to...; used to ask about the addressee's intentions, often with a nuance of slight surprise.

   are you going to...; used to ask about the addressee's intentions, often with a nuance of slight surprise.

   Used sarcastically to deny the possibility of something being true by positing an equally absurd situation.

   Used to invite someone to guess.

   In the familiar style, the principal imperative suffix.

   alternative form of -개 (-gae, “[agentive suffix]”)

   short for -에게 (-ege, “to”)

   Source: wiktionary.org