“Well, I appreciate your honesty.”
A friend told you something negative about yourself, but you're glad because now you know how she feels. You say this to her.
Well, I appreciate your honesty.
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(someone) appreciates (something)
When you "appreciate" something, it means that you notice it and are thankful for it.
You say "I appreciate ___" or "We appreciate ___" when you want to thank someone for their actions. This phrase sounds more clear and explicit than just saying "Thank you for ___".
We really appreciate all of your hard work and effort.
I appreciate everything you've done for us. You've been so helpful.
I appreciate your honesty.
This is a set phrase that people say when someone tells them something bad. You say this to show that, although you don't like to hear that, you are glad that the person was honest.