Yojijukugo are four-character compound Japanese words, often expressive idioms. The direct translation is four (四) character (字) idiom (熟語). A beautiful part of the Japanese language (and culture!), they carry much meaning in little space. Brevity is the soul of wit, someone said. According to jisho.org, Japanese has over 3000 yojijukugo.
Another aspect of yojijukugo is that they often evoke powerful metaphors and analogs to convey their meaning. For example, the equivalent of "survival of the fittest" in Japanese is 弱肉強食 (jakunikukyoushoku). The literal translation is weak (弱) meat (肉) strong (強) food (食). Isn't that a fun way of putting it?
Yojijukugo I treasure
Translation: Unaffected and sincere, with fortitude and vigor.
質 (shitsu) on its own can mean quality, value, or nature. 実 (jitsu) on its own can mean truth, sincerity, or honesty. 剛 (gou) on its own means robust or strong. 健 (ken) on its own might mean healthy or fit.
But, if you instead parse it as two words:
質実 (shitsujitsu) is a word meaning simplicity. 剛健 (gouken) is a word meaning vigor.
I admire that regardless of at which level of granularity you resolve the components of this word, they always seem to add meaning to the yojijukugo.
Direct translation: one day, one step.
I like the imagery: every day, taking a single step. Slow but steady.
Direct translation: one time, one meeting.
This one is more difficult to translate naturally. I think of it as a mix of "once-in-a-lifetime" and "nothing should go left uncherished". By "one time, one meeting", it means to say that you'll only get to experience every thing once. By underscoring the finiteness of our experiences, it asks of us to cherish each of them.
Natural translation: playing it by ear.
臨機 (rinki) means tailor-made or suited to the occasion. 応変 (ouhen) means to respond to change.