I haven’t memorized my new postal code yet.
You know that a 郵便 is the mail and that a 番号 is a number. So a "mail number," what is that? Usually refers to your post number or postal code. It is also often referred to with a symbol, which is 〒, so look out for that.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.