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As a native English speaker in North America, it does perhaps sound a tad odd, but that's a hard call to make without reading it in context. Several thoughts:

  • if you want to keep the word "way", I would use the infinitive: "way to clean"
  • if you like "method", I would use "of": "method of cleaning"
  • the most natural to me, without any other context, is "they taught us how to clean"