'to let down' means to disappoint someone.
- I promised to do it, I can't let her down.
- They let us down badly by not completing the work on time.
'to let in' means to allow someone to enter.
- I have a front door key. I can let myself in.
- They're at the door. Can you let them in?
'to let in' can also mean to allow water, light or air into something which is normally sealed.
- I opened the curtains to let in the sunshine.
- I need some new boots for winter. These let water in.
'to let in for' means to be involved in something difficult or unpleasant.
- This job is very hard. I didn't realise what I was letting myself in for.
- She didn't realise how much work she was letting herself in for doing this course.
'to let in on' means to tell someone about something which is secret.
- I don't know what they're doing. They wouldn't let me in on their plans.
- She let me in on her secret. She's getting married!
'to let off' means to not punish someone when they have done something wrong.
- He was caught smoking in the office but they let him off because it was the first time.
- I'll let you off this time but if you do it again, you'll be severely punished.
'to let off' can also mean to allow someone to not do something they should do.
- I owed him some money but he let me off. I didn't have to pay him back.
- I was supposed to work until 10 pm but my boss let me off at 9.
'to let out' means to allow someone to leave a place, usually by opening a door.
- He stopped at the traffic lights to let me out.
- Let me out at the end of the road. I can walk the rest of the way.
'to let out' means to make a particular sound.
- When she heard the news, she let out a huge sigh of relief.
- They all let out a groan when they heard the bad news.
'to let up' means to cease or to decrease in intensity.
- We'll go out for a walk if the rain lets up.
- The pressure at work is non-stop. It never lets up.