Your coworker is trying to change the color of some text on a spreadsheet document on his computer, but can't figure out how to do it. You think you know how, so you say this.
Here - let me take a look.
People often say "here" before offering to help or take responsibility for something. A few more examples:
Here - let me do that
Here - I'll hold this while you tie it up.
The word "look" is very general. It can mean to look for a long time, a short time, carefully, absent-mindedly, or in many other ways. "Take a look" is more specific. It means to look at something for a short period, usually for a specific purpose.
You can ask someone to take a look at something that needs to be fixed, or for something that's important for them to see. Here's another example from a science classroom. The teacher tells the class to look at something in the textbook:
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