I can't be sure because you haven't provided a reproducible example (I don't know from where the Hotel Bookings data frame comes from), but I think this is what you want to do.
bookings %>%
filter((arrival_date_year == 2015 | arrival_date_year == 2016),
arrival_date_month == "June",
reservation_status != "Canceled")
If this doesn't solve your problem, please provide a proper REPRoducible EXample (reprex) illustrating your issue.