Summary of Findings
This claim is true. The original source comes from an article published by Nature Reviews Earth and Environment, an online reviews journal. The authors of the review article, "The environmental price of fast fashion", are professors and researchers that specialize in design, economics, sustainability, and the social sciences (Niinimaki et al. 2020). The numbers included in this article have also been reported by news outlets, government resources, international reports, and independent research groups. Niinimaki has also been published several times on this topic.
Sources and Evidence
https://www.nature.com/articles/s43017-020-0039-9
Original article published in Nature Reviews Earth and Environment. Authors Niinimaki et al. claim that the fashion industry produces more than 92 million tons of waste each year and consumes 79 trillion liters of water annually. The authors also claim that the fashion industry contributes heavily to global carbon emissions and greenhouse gas levels.
https://www.nature.com/natrevearthenviron/journal-information
The Journal, Nature Reviews Earth and Environment, describes itself as "interested in the latest advances in, and timely syntheses of, research spanning all aspects of Earth and environmental science."
https://unfccc.int/news/un-helps-fashion-industry-shift-to-low-carbon
The article cites this source from the UN Climate Change website, which supports the claim that fast fashion contributes 10% of global greenhouse emissions.
https://www.carbontrust.com/sites/default/files/documents/resource/public/International%20Carbon%20Flows%20-%20Clothing%20-%20REPORT.pdf
The article also sites this report from Carbon Trust, which supports the claim that fast fashion accounts for approximately 3% of global carbon emissions.