Learn Turkish: Terliklerim nerede? - Where are my slippers?

If you said "my slipper" (singular), the k would change because you're adding a vowel suffix directly to it: terlik + -im = terliğim. But here, the plural suffix -ler comes first. The possessive suffix -im attaches to the r in terlikler, so the k doesn't touch a vowel and stays exactly as it is.

Why is it nerede and not nereye?

You use nerede (where at) when asking for a static location, using the locative suffix -de. You would use nereye (where to) if you were asking about direction or movement, like "Where are you going?". Since the slippers are just sitting somewhere, nerede is the correct choice.

Since "terliklerim" is plural, shouldn't we add a plural suffix to the question word and say neredeler?

You don't need to! In Turkish grammar, when the subject is non-human (like animals or objects), the verb or predicate usually stays in the singular form, even if the subject is plural. While neredeler isn't strictly wrong, nerede sounds much more natural for objects like slippers.