What version of ImageMagick? What platform/OS?
magick composite is not as flexible as just magick for doing compositing. You should start using that.
Your pattern image has transparency. So you should be using -compose copy_opacity -composite with magick using its alpha channel and putting that alpha channel into the alpha channel of the green image.
Unix syntax:
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magick green.png \( pattern.png -alpha extract \) -alpha off -compose copy_opacity -composite result.png
Window syntax:
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magick green.png ( pattern.png -alpha extract ) -alpha off -compose copy_opacity -composite result.png
If you really want multiply, then
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magick green.png \( pattern.png -alpha extract \) -compose multiply -composite result.png
or
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magick green.png \( pattern.png -alpha off \) -compose multiply -composite result.png
Since the alpha channel is the same as the pattern image base channels.
But then the result will have a black background.