How do I say pack my luggage in Japanese?
Do I say 荷物を片付けます?

Question

Answer

Or you may also say 「荷造りをする」

荷造り（にづくり）= n.
荷造りをする = v.

Recently some people use the term 「パッキング」as well.
(just like "packing" in English)

パッキング = n.
パッキングをする = v.

Answer

僕の場合は，「荷物をまとめる」の言葉を使う。

Answer

If you say 片付ける, many Japanese think you put away or organize something. If you say 荷物をまとめる, you can make yourself understood. Good question!