farblich
color-wise
Concerning the color or color scheme; with regard to color.
Die Kissen sind farblich genau auf das neue Sofa abgestimmt.
The cushions are color-coordinated exactly with the new sofa.

color-wise
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color-wise
Concerning the color or color scheme; with regard to color.
Die Kissen sind farblich genau auf das neue Sofa abgestimmt.
The cushions are color-coordinated exactly with the new sofa.

The word is made up of the noun 'Farbe' (color) and the ending '-lich'. It literally means 'concerning the color' or 'with regard to color'.
Wir müssen die Vorhänge noch farblich an die Wandfarbe anpassen.
We still need to match the curtains to the wall color.
'Farblich' (color-wise) is almost always used as an adverb to modify a verb or another adjective. Using it directly before a noun, e.g. 'ein farbliches Muster', is very rare and sounds unnatural.
Die Blumen im Garten sind farblich sehr schön arrangiert.
The flowers in the garden are arranged very beautifully in terms of color.
Common verbs combined with 'farblich' (color-wise) are 'abstimmen' (to coordinate), 'passen' (to match), or 'sortieren' (to sort). This expresses that colors harmonize or are being organized.
Die beiden Pullover passen farblich überhaupt nicht zusammen.
The two sweaters don't match at all in terms of color.
colorful
'bunt' and 'farblich' both have to do with colors, but they do not describe the same thing. 'bunt' says that something has many different colors or looks colorful. 'farblich' means: with regard to color or the color scheme. It is often used when colors match, are compared, or are planned. Learners may confuse the words because both appear in contexts involving clothing, pictures, or rooms. As a practical rule: if you see many colors, 'bunt' fits. If you are talking about the effect or coordination of the colors, 'farblich' fits.

Die neuen Vorhänge passen farblich gut zum Sofa.
The new curtains go well with the sofa color-wise.
Meine Freundin trägt heute ein buntes Kleid mit roten, blauen und gelben Blumen.
My friend is wearing a colorful dress today with red, blue, and yellow flowers.