Complex sentence: Hamilton was the Colonel of the 15th Regiment of Foot from 22 August 1792 to 1794, during which he took part in the 1790s West Indies Campaign.
Split into simpler sentences: Hamilton was the Colonel of the 15th Regiment of Foot from 22 August 1792 to 1794. During his time with the 15th Regiment, Hamilton was a part of the 1790s West Indies Campaign.