can we restore a database from mongodb 4.4 version to mongodb 6.0.13 directly

Please help me out with the subjected matter

It depends

Database files / volume snapshot - no. This can be started with MongoDB 4.4 and 5.0(if the FeatureCompatibilityVersion was at 4.4)

Mongodump - Maybe. Officially mongodump/mongorestore is only for the version of the tool mongodump with the version of the database it was taken from. But many have success.

I prefer to use the same version to restore and then upgrade.Compatibility and feasibility are the highest.