A team can play a maximum of 28 games in a single NHL playoff run.
That total comes from the Stanley Cup Playoffs’ four-round structure. Each round is a best-of-seven series, so a team that reaches the Stanley Cup Final and needs all seven games in every round would play 7 × 4, or 28 games.
A team can reach the same championship destination in fewer games by sweeping an opponent or winning a series in five or six games. The 28-game figure is therefore a maximum, not the usual workload. It counts games played by one team, rather than the total number of games across the entire postseason.
The modern playoff bracket has 16 qualifying teams, with eight teams in each conference. The first two rounds are conference-based, followed by the conference finals and Stanley Cup Final. The format has changed over NHL history, but 28 is the standard answer for the current best-of-seven system.