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Please teach me how to starch clothes with laundry starch.
Literal
Laundry-starch [with-で] [genitive-の] starching [genitive-の] way [object-を] please-teach.
A household how-to question. The particle sequence での is a composite: で (instrumental 'with/using') + の (attributive genitive). Together they turn an instrumental phrase into a noun-modifier: 洗濯のりでの + のりづけ = 'starching (done) with laundry starch.' This is a productive construction — 鉛筆での書き方 ('writing with a pencil'), 日本語での会話 ('conversation in Japanese'). The noun 仕方 ('way,' 'method,' 'how to') attached to a verb stem with の turns it into a 'how-to' — のりづけの仕方 = 'how to starch.' 洗濯のり ('laundry starch') is a household product.