The previous post is linking to a deleted topic. The significant content of the post that was linked to is to first go to your Admin / Customize / Text page and search for 'YY
That will return the following list:
js.dates.tiny.date_year
MMM 'YY
js.dates.medium.date_year
MMM D, 'YY
js.dates.long_date_with_year
MMM D, 'YY LT
js.dates.long_date_with_year_without_time
MMM D, 'YY
js.dates.long_date_with_year_with_linebreak
MMM D, 'YY <br/>LT
Edit each of those entries to replace 'YY
with YYYY
to get the full year.