Learn Dutch: Kun je eventjes buiten wachten? - Can you wait briefly outside?

Eventjes is the adverbial diminutive of even (briefly or for a moment). Adding -tjes makes the request sound softer, friendlier, and more casual. It minimizes the imposition on the person you are asking to wait.

Why does eventjes come before buiten?

This follows the standard Dutch word order rule of Time before Place. Eventjes tells us how long (time), and buiten tells us where (place), so the time word must appear first in the sentence.

Why is the suffix -tjes used instead of just -jes for this word?

When a base word ends in an unstressed syllable ending in -n (like the second syllable of even), the diminutive suffix becomes -tjes instead of -jes. This simply makes the pronunciation flow more naturally.

Could I use zachtjes or stilletjes instead of eventjes in this sentence?

You could, but it changes the meaning entirely. Eventjes is an adverb of time (briefly). Zachtjes (softly) and stilletjes (quietly) are adverbs of manner. If you asked Kun je stilletjes buiten wachten?, you would be telling the person to wait outside in complete silence!