This is the 9679th most frequent Polish word.
zachodowi
"Zachodowi" means "to the West" or "for the West" in English, depending on context.
Here 'zachodowi' means 'to the West' and is in the dative case, expressing the indirect object of the verb 'podziękowaliśmy' (we thanked).
Podziękowaliśmy zachodowi za gościnność.
We thanked the West for their hospitality.
In this example, 'zachodowi' refers to 'to the West' and functions as an indirect object indicating the recipient of the action.
Mapa wskazuje zachodowi kierunek do celu.
The map shows the direction to the West.
'Zachodowi' is used as an adjective form ('Western') here, describing 'ludzie' (people), though it resembles the dative case in form; context differentiates its usage.