Segment Information - Schedule of Segment Reporting Information (Details) - USD ($) $ in Thousands	3 Months Ended
	Sep. 30, 2024	Sep. 30, 2023
Segment Reporting Information [Line Items]
Net sales	$ 394,596	$ 425,029
Adjusted EBITDA	22,375	24,090
Depreciation and amortization	(11,427)	(12,305)
Equity in net loss of equity-method investees	(155)	(498)
Interest expense, net	(12,995)	(12,623)
(Provision) benefit for income taxes	(3,523)	5,379
Stock-based compensation, net	(2,876)	(3,742)
Unrealized currency losses	(1,194)	(35)
Certain litigation expenses, net	(827)	(1,524)
Acquisitions, divestitures and other
Loss on sale of assets	(3,934)	(62)
Transaction and integration costs, net	318	(118)
Impairment charges
Long-lived asset impairment	(31)	(694)
Net loss	(19,663)	(10,376)
Plant closure related costs, net
Restructuring activities
Restructuring activities	(376)	(1,841)
Productivity and transformation costs
Restructuring activities
Restructuring activities	(5,018)	(6,403)
Operating Segments
Segment Reporting Information [Line Items]
Net sales	394,596	425,029
Adjusted EBITDA	32,829	36,165
Operating Segments | North America
Segment Reporting Information [Line Items]
Net sales	231,140	260,054
Adjusted EBITDA	12,459	18,727
Operating Segments | International
Segment Reporting Information [Line Items]
Net sales	163,456	164,975
Adjusted EBITDA	20,370	17,438
Corporate and Other
Segment Reporting Information [Line Items]
Adjusted EBITDA	$ (10,454)	$ (12,075)