Learn Finnish: Lähdemme mahdollisimman kauas etelään. - We are leaving as far away to the south as possible.

Mahdollisimman is the genitive form of the superlative adjective mahdollisin (the most possible). In Finnish, you put mahdollisimman directly in front of a basic (positive) or comparative adjective or adverb to mean "as [word] as possible". Here, it pairs with the adverb kauas to mean "as far as possible".

Why does the sentence use kauas instead of the static word for "far", kaukana?

Finnish location adverbs change form depending on movement. Because the verb lähteä (to leave) implies movement towards a destination, we must use the directional form kauas (far to). Kaukana means "far away" in a stationary sense (far at), which wouldn't work with lähteä.

Could we just say mahdollisimman etelään to mean "as far south as possible"?

No, you cannot use mahdollisimman directly with a noun like etelä (south). The word mahdollisimman must modify an adjective or an adverb. That is why the directional adverb kauas is required here as a bridge: mahdollisimman kauas etelään literally translates to "as far away as possible into the south".

Why is etelään in the illative case?