The doctrine of nullification led to the philosophy of "manifest destiny." Is this True of False?

I don't think that's true because nullification and manifest destiny are two completely different topics.

Nullification states that a state has the right to deem any federal law unconstitutional and nullify it or declare it invalid and manifest destiny is the belief that all Americans were destined to expand throughout the continent.

It is false. The doctrine of nullification most certainly did not lead to the philosophy of manifest destiny.