Step 1: Apple.
Apple is commercially propagated by tongue grafting, correlating to A - II.
Step 2: Litchi.
Litchi is propagated by air layering, correlating to B - I.
Step 3: Ber.
Ber is propagated by hardwood cuttings, correlating to C - III.
Step 4: Grapes.
Grapes are commercially propagated by T-budding, correlating to D - IV.
Step 5: Conclusion.
The correct matching is: A - II, B - I, C - III, D - IV.