Refers to the visual pattern or design on a surface, especially in art, textiles, or printed materials.
The pattern on this kimono is very beautiful.
This cup has a floral design on it.
I choose the design for a new smartphone case.
I chose a postcard with a design I liked.
This kimono has a very gorgeous pattern.
デザイン is a loanword used for modern or industrial design work, whereas 絵柄 is more traditional and focused on the visual motif itself.
図案 refers to a design sketch or plan created for a purpose, while 絵柄 refers to the finished pattern as it appears on an object.
絵柄 refers specifically to a pictorial or illustrative design (like a printed picture), while 図柄 covers designs more broadly, including abstract or geometric patterns.
Compound of 絵 (e, 'picture') and 柄 (gara, 'pattern'). The reading えがら is a standard kun'yomi combination.