Question: Where are three-month-old or possibly even year-old Himawari weather satellite images available to the public?
As an exercise, per:
the event was at 2018-12-18 23:48:20 UTC and 56.9N 172.4E.
Presuming research you can obtain Himawari images from the following institutions as mentioned in the original link I provided
The following four Japanese institutions operate Himawari-8 data archiving and redistribution services on a best-effort basis for research, development and education:
1) JAXA Himawari Monitor (Japan Aerospace Exploration Agency) http://www.eorc.jaxa.jp/ptree/index.html Himawari-8 Data Download and Processing System (Data Integration and Analysis System Program)
2) http://himawari.diasjp.net/expert/ Center for Environmental Remote Sensing (CEReS)
3) Chiba University http://www.cr.chiba-u.jp/databases/GEO/H8_9/FD/index_jp.html
4) Himawari Satellite Project (NICT : National Institute of Information and Communications Technology) http://sc-web.nict.go.jp/himawari/
Users must register to download data from each institution and observe the individual data usage policies.
If you are asking how I would do it then I must mention I use a python software called SatPy
Then I go to this URL - JAXA FTP URL( I think it is only visible if you are registered) and then download the data for whatever year I want. Then write a small script using a SatPy reader and view the data.
NOTE For the last points you are better off asking questions either on SatPy and for the data itself writing email to JAXA.