"The world is an effect and hence it must have an efficient and intelligent cause. That efficient and intelligent cause is God." Which means of knowledge is used in this argument as per classical Indian School of Logic (Nyaya)?

The claim moves from an observed mark, the world being an effect, to an unseen conclusion, an intelligent cause called God.

This is reasoning from a sign to what it invariably accompanies.

In Nyaya such passage from a known reason to a probandum through concomitance is inference.

The world as effect serves as the middle term leading to a designing cause.

So the means of knowledge here is anumana, inference.