the week of (date)

When you need to refer to a specific week, you can pick a day that falls during that week, and call it "the week of (that date)":

I think we're coming the week of June 4th.

Usually you use the first day of the week (Monday) as the date in this expression. But you can also use other days of the week. If you only remember one date during that week, you can use that date, whether it's the first day of the week or not.

I'd like to (do something)

"I'd like to..." is an abbreviation of "I would like to..." Use this phrase to ask for services at stores, banks, and so on:

Hi. I'd like to deposit this into checking, please.

I'd like to send this via registered mail.

I'd like to cancel my membership.

You can also use it in an email to someone when you're in a position of authority, like when you're acting as a customer.

It's also possible to write "I'd like to ___" in emails to your boss, if you're doing something that's normal and expected. For example, if you have a specific number of vacation days that you can use, and you're allowed to use them whenever you want, you can write:

I'd like to take off the week of April 3rd.

let me know

The phrase "Let me know ___" means "Tell me ___". It's extremely common in everyday English, because "Tell me ___" can sound too demanding or angry.

Here are some examples:

Let me know when you're free and we'll set up a meeting.

Let me know when you hear from them.

If you encounter any problems, please let me know immediately.

You can see "Let me know..." a lot in business emails.

take off (time from work)

"Taking off" time from work means taking an allowed vacation or personal day.

For example:

Can I take off next week?

I'm thinking about taking off this Thursday afternoon for a doctor's appointment.

The phrase "take off" can be split up:

Why don't you take tomorrow off?

(something) presents a problem

When there's a problem with a situation, you can say that the situation "presents a problem".

For example, if one of your employees wants to take a vacation on a day when something important needs to be done, you can say:

Actually, that presents a problem.

Another example:

Borrowing my hair dryer is fine, but you borrowing it and not returning it presents a problem.

This is a somewhat formal phrase.