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I have wriitten the sentences below.

(1a) Most of these complicated designs can be made by knitting or embroidering them. (my own sentence)

(1b) Most of these complicated designs can be made by knitting or embroidering. (my friends' revision)

(2a) Professionals can make most of these complicated designs by knitting or embroidering. (my own sentence)

(2b) Professionals can make most of these complicated designs by knitting or embroidering them. (my friends' revision)

If my non-native English speaking friends are correct, I don't understand why you don't need "them" in (1a) and you need it in (2a). Please help me. Thank you very much for your time.

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Sorry, but I have done knitting, embroidery, crewel work, crochet, macramé and even quilting in my younger days.

I cannot imaging a complicated design that can be both knitted and embroidered. These are completely different techniques and concepts in fabric art. Can you show us a picture of what you are talking about?