What time is best for you for the next meeting? Your time zone is fine.
What is the most convenient time for you in your local time zone?
What is the best time in your time zone for the next meeting?
時差はやっかいですね。海外とのミーティングの設定はきちんと伝えて確認しないと大変なことになります。サマータイムを導入している国になるとますますややこしい。
そちらの時間帯：your time zone / your local time zone
your time と言うよりもこう言う方が聞く側にとってもわかりやすいです。
決定したあと、再度相手と確認する場合は、多少面倒でも相手と自分の時間をしっかり確認した方が間違えが起こりません。例えば、
「次回のミーティングはそちらの時間で午後五時、こちらの時間で午前八時ですね。」
Let me make sure that our next meeting will be 5 PM in your time zone, and 8 AM in my time zone.
5PM / 8AMの部分とin your time /in my timeのyour / myの部分をより強調してちょっとゆっくり言うと相手も聞いて確認しやすいです。
In your local time, when would be a convenient time for our next meeting?
You can also say the name of the country. For example, you can say, "according to Taiwan local time, what time would be convenient for our next meeting?"
その国の名前を用い表現するといいかと思います。"according to Taiwan local time, what time would be convenient for our next meeting?"台湾の時間では、次のミィーティングは何時が都合が良いですか？このようになります。
When will be the best time for our next meeting? kindly give me the time in your your local time zone.
What time would be convenient for our next meeting? I would prefer if you give me the time in your local time zone.
->When will be the best time for our next meeting? kindly give me the time in your your local time zone.
->What time would be convenient for our next meeting? I would prefer if you give me the time in your local time zone.
>Both of the above phrases above are good to use. Both clearly indicate that you want the time in their local time zone.
->When will be the best time for our next meeting? kindly give me the time in your your local time zone.
->What time would be convenient for our next meeting? I would prefer if you give me the time in your local time zone.
上のフレーズは使いやすいです。どちらも彼らの時間帯に合わせたいということをはっきりと示しています。
What time is convenient for you for our next meeting in your time zone?
The sentences above means that you want to know the time they will be able to attend the next meeting.
You are also saying that if they give you the time in their time zone you okay with it.
In your local time zone, what time is most convenient for you for the next meeting?
What time would be best for you in your local time zone?
When you ask someone 'in your local time zone' they will give you the time according to the time zone of the area they live in. This clears any confusion because you already stated that it's their time you are concerned about. This expression is very good when communicating with people overseas because different time zones can cause a lot of confusion especially when scheduling meetings, so you have to be clear regarding whose time zone you will follow.
"in your local time zone" と言えば、相手が住んでいる地域のタイムゾーンの時間を教えてくれます。あなたが相手の時間帯を気遣っているということを既に言っているので、こう言うことで混乱を避けることが出来ます。
この様な表現は、海外の人と話す時はとても良いです。というのも特に会議のスケジュールを決める時にタイムゾーンが違うと多くの混乱が生じる可能性があるからです。ですからどのタイムゾーンについて言っているのかを明確にする必要があります。
アメリカ合衆国 
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