"How often would you like me to clean this place?"
"Would you like me to clean this place every time?"
When using these phrases you are asking the owner if they want you to clean this certain place every time, or how frequently should I clean this place?
"How often would you like me to clean this place?"（ここはどのくらいの頻度で掃除すればいいですか）
"Would you like me to clean this place every time?"（ここは毎回掃除した方がいいですか）
ここでは、その場所を
例1）どのくらいの頻度で掃除したらいいか
例2）毎回掃除した方がいいのか
と尋ねています。
I find 'would' rather than 'should' to be more polite to a new person you are talking to.
How you address the place you want cleaned could also change but limit it to meaning a specific placement. If it is a room you are asking,, its easy to simply say this area. While if speaking more generally, maybe a home, you could say simply' this'. But its best to be near the area you are asking about when using 'this.'. Since the person already knows what you are talking about, you can be more general.
Would you like me to clean this every day? That would be fine.
Do you want this cleaned every day? Yes, I do.
How often do you want it cleaned? Every day.
"Would you like ..." is a polite way to ask someone what they want. "Would you like me to clean this every day?" is an indirect question which is a more polite way of speaking.
"Do you want this cleaned every day?" is more direct, but since it is in the Passive Voice it also sounds polite, more polite than saying do you want me to clean this every day?
"How often do you want this cleaned?" leaves it open for the person you're asking to say exactly how often they want it done. It is polite and does not make an assumption about what the person may want.
"Would you like ..." は、相手の求めることを尋ねる丁寧な表現です。
"Would you like me to clean this every day?"（ここは毎日掃除した方がいいですか）は、間接的な質問で丁寧です。
"Do you want this cleaned every day?"（ここは毎日掃除した方がいいですか）は、より直接的な言い方ですが、ただこれも受け身を使っているため丁寧です、"Do you want me to clean this every day?" よりも丁寧です。
"How often do you want this cleaned?"（ここはどのくらいの頻度で掃除したらいいですか）では、頻度を相手に委ねています。これは丁寧な言い方で、相手の求めることについて臆測せずに尋ねています。
How often is referring to when to clean this, clean it often or not so often, a lot or not so much.
would you like and when would you like are very common phrases to word this particular sentence together, with the same objective.
how often' はそこを掃除する頻度を言っています。頻繁に掃除するのか、それほどでもないのか。
'would you like' と 'when would you like' はこの文を組み立てるときの非常に一般的なフレーズです。尋ねていることは同じです。
If you are unsure of how often you should clean someehere then you could ask 'should I clean this place/here every day? or 'how often should I clean here?'
どのくらいの頻度でそこを掃除すればいいのか分からないときは、次のように言えます。
'Should I clean this place/here every day?'（ここは毎日掃除した方がいいですか）
または、
'How often should I clean here?'（ここはどのくらいの頻度で掃除すればいいですか）
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