Sino-Vietnamese word from 松 (“pine”), 菊 (“chrysanthemum”), 竹 (“bamboo”) and 梅 (“plum, apricot”), said to represent "winter", "autumn", "summer", "spring" respectively.
Compare the concepts of Flowers of the Four Seasons and Four Gentlemen.
Certain sources explain the reverse order of the seasons as due to European influence, where paintings (and writings, etc.) are views from left-to-right, as opposed to the traditional order in the Sinosphere, being right-to-left. However, this is far-fetched as tùng cúc (“pine and chrysanthemum”) and trúc mai (“bamboo and apricot”) are both common motifs in Vietnamese literature long before European influence, signifying a person's spirit, and intimate bonds, respectively (and both also seems to be borrowed from/influenced by Chinese literature).
Most likely this phrase was just amalgamation of those two compounds above, then forcefully made to fit with similar concepts to which it shares several elements (see 松竹梅 (tùng trúc mai)), even if the order of seasons is reverse.