Gary, who is single, sells his principal residence $($owned and occupied by him for $5$ years$).$ in November $2023$ for a realized gain of $$178,800.$ He had purchased a more expensive new residence eight months prior to the sale. He anticipates that he will occupy this new house as his principal residence for only about $22$ additional months. He expects it to appreciate substantially while he owns it$.$ Gary would like to recognize the realized gain on the $2023$ sale to offset a large investment loss from the sale of stock.

Can he recognize the realized gain of $$178,800$ on the sale of his principal residence in $2023?$