The most common and most likely answer to this crossword clue is the 12 letter word CROSS-STITCH
I've seen this crossword clue in The Times
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More clues leading to the result CROSS-STITCH
Buddy explains!

The straight part
We know that "Embroidery done a certain way" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case embroidery done a certain way = cross-stitch.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CROSS-STITCH mean?
CROSS-STITCH noun- A double stitch that forms a cross.
- Embroidery or needlework made using such stitches.
- To embroider with such stitches.