Other Expense, Net - Schedule of Other Expense, Net (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Mar. 31, 2024	Mar. 31, 2023	Mar. 31, 2024	Mar. 31, 2023
Other Income and Expenses [Abstract]
Unrealized gains on company-owned life insurance contracts and investments held in rabbi trusts	$ (2.5)	$ (1.5)	$ (5.0)	$ (2.1)
Interest income	(0.1)	(0.1)	(0.4)	(0.2)
Foreign exchange (gains) losses	(0.1)	(0.1)	1.3	1.1
Pension earnings, interest and deferrals	3.7	2.5	10.6	7.5
Pension settlement charge	51.9	0.0	51.9	0.0
Other	0.0	0.0	0.1	(0.1)
Total other expense, net	$ 52.9	$ 0.8	$ 58.5	$ 6.2