The thousand and the ten thousand are not counted but piled up, the way the dictionaries put it: many, and more. The phrase is Japanese, made out of Chinese parts by people who painted signs; no Chinese text we have searched has the four characters together.
Brushed for a new shop, the word goes back onto the door it was made for.
The four-character idiom 千客万来 is composed of the kanji 千 (read sen) meaning "thousand", 客 (read kyaku) meaning "customers", 万 (read ban) meaning "ten thousand" and 来 (read rai) meaning "visits".
The term is used as a wish for "doing a roaring business" or for "a constant stream of customers".
千客万来 is a Japanese-made shop-sign phrase with no Chinese source, first found in 1805 in 萩庵荻声's comic picture-book 茶漬原御膳合戦, where a famous sign-painter writes it on the lantern of a crowded tea-and-rice shop on the Shinagawa road; by 1811 it hung on storytelling halls and was joked about in senryū.
We want you to be as happy with the meaning as you are with Master Takase's art. To learn more, visit Philology of 千客万来.