Across: అడ్డంగా/ మీదుగా...
Through: ద్వారా/ గుండా...
The difference between ACROSS and THROUGH is similar to the difference between ON and IN. We use THROUGH to talk about movement in three dimensional spaces with things on all sides.
🔹We walked across the field. (= We were on the field.)
🔹We walked through the wood. (= We were in the wood.)