染色 and 刺繍: dyeing cloth and embroidering a red flower
Compare 染色 with plant-derived color and 刺繍 of a red flower on white cloth, keeping an exhibit’s introduction and a pouch’s use distinct.
染色: dyeing with plant color and introducing techniques
「植物から取った色で布を染色した。」 means “We dyed the cloth with color extracted from plants.” 染色（せんしょく） means dyeing. 植物から取った色で supplies the source of the color used here, while 布を染色した is the action of dyeing the cloth.
「展示では地域に伝わる染色の技法が紹介されている。」 means “The exhibit introduces dyeing techniques handed down in the region.” 地域に伝わる染色の技法 names dyeing techniques handed down in the region. 紹介されている is their introduction at the exhibit; it is not an action of dyeing performed by a visitor.
刺繍: a flower on white cloth and a treasured pouch
「白い布に赤い花を刺繍した。」 means “I embroidered a red flower on white cloth.” 刺繍（ししゅう） means embroidery. 白い布に gives the white cloth as the background, and 赤い花を names the red flower embroidered on it, without adding an earlier step of dyeing the cloth.
「祖母の刺繍が入った袋を大切に使う。」 means “I take good care of the pouch embroidered by my grandmother.” 祖母の刺繍が入った袋 identifies the pouch with the grandmother’s embroidery. 大切に使う describes caring for and using that pouch; the user is not thereby made the embroiderer or the maker of the whole pouch.
Putting color into cloth and stitching a flower onto it
布を染色した describes dyeing the cloth with color extracted from plants. 白い布に赤い花を刺繍した describes embroidering a red flower on white cloth. The shared cloth background does not make the two actions identical.
Introducing techniques at an exhibit and using a pouch with a grandmother’s embroidery are distinct from personally dyeing or embroidering. An introduction to a technique or care for a finished item does not by itself establish that person’s creation of the item.
What was done to the cloth in 植物から取った色で布を染色した and 白い布に赤い花を刺繍した?
Show the answer and why
The first sentence describes dyeing the cloth with color extracted from plants. The second describes embroidering a red flower on white cloth. The separate exhibit example does not say that visitors performed those techniques themselves.