Learn Turkish: Yoğunluktan dolayı misafir gecikti. - The guest was delayed due to the rush.

The postposition dolayı (meaning "due to" or "because of") always requires the preceding noun to be in the ablative case (the "from" case, usually -dan or -den). Because yoğunluk ends in a hard consonant (k), the suffix mutates to -tan.

How is the word yoğunluk formed?

It comes from the adjective yoğun, which means "dense", "intense", or "busy". Adding the suffix -luk turns it into an abstract noun, so yoğunluk means "density", "busyness", or in this context, "the rush" (like rush hour traffic).

The lesson also mentions ötürü. Could I use it in this sentence?

Absolutely. Dolayı and ötürü are exact synonyms meaning "due to" or "because of", and both require the ablative (-dan / -den) case. You can say yoğunluktan ötürü and it will mean exactly the same thing.

Could I say misafir geç kaldı instead of misafir gecikti?

Yes, both are common ways to say someone is late. Gecikmek is a single verb meaning "to be delayed" or "to run late", which focuses slightly more on the process of being held up by something (like the rush). Geç kalmak simply means "to be late".