Learn Hardcore Korean: geotgi jeone mureul masyeoyo.

The suffix -기 is a nominalizer. It turns the verb 걷다 (to walk) into the noun-like form 걷기 (walking). Only a noun or nominalized verb can take the postposition 전에 (“before”).

Why is it 걷기 전에 and not 걷다 전에?

전에 attaches to nouns or nominalized verbs, not to the basic verb form 걷다. You must first add -기 to make 걷기, then attach 전에 to mean “before walking.”

What exactly does 전에 mean here?

전에 is a postposition meaning “before” in terms of time. When you say 걷기 전에, you literally mean “before (one’s) walking.”

Why is it spelled 걷기 with the ㄷ intact, rather than changing to 걸기?

Korean has some ㄷ-irregular verbs (like 걷다) that change ㄷ → ㄹ before a vowel ending (e.g. 걷다 + 어요 = 걸어요). But -기 begins with a consonant ㄱ, so the irregular rule doesn’t apply and the original ㄷ remains, giving 걷기.