What does "I'm catching a 4:00 at Logan" mean?
Solution 1:
Logan is an airport in Boston.
"A 4:00" means a 4:00 flight. That style of reference is often used for "commuter" flights, which go a particular route at a scheduled regular interval, e.g., every hour on the hour during certain parts of the day. So "catching a 4:00" refers to planning to take the one scheduled to leave at 4:00.
He's relying on a taxi to get him to the airport. He's looking out the window and there isn't one, so he's concerned about how he will get to the airport in time for his flight.