Japanese loves to make words shorten. Specially the young people.
What does [Akeome] mean?
[Akeome] is abbreviation of “Akemashite Omedeto gozaimasu” 「Happy New Year」
What does 「Koto Yoro」mean?
「Koto Yoro」is abbreviation of “Kotoshi mo yoroshiku onegai shimasu” 「 I look forward to your continued good will in the coming year」「Kotoshi mo yoroshiku onegai shimasu」is the stereo type common phrase used after happy new year in Japan. It has many meanings. In English people normally say after Happy new year, wishing you all the best etc. Or it depends on whom you are addressing to. May be “I look forward to seeing you again this year”, “I hope we all prosper this year”, “I look forward to spending as much time this year as last year” and so on.
“Hon nen mo dozo yoroshiku onegai moushi agemasu” is a formal way of greeting.
During first three days, people might wear kimono greeting to families, friends and visiting temples and shrines.
Hope it is informative and interesting to you.