A 100-meter-long wire mesh is available to fence a region like the one in the figure. What are the values of x and y that make the enclosed area maximum?

There's nothing that identifies what the figure looks like.

In any event you need to start by what you tried to far.
Since you haven't given specifics (i.e a diagram that identifies x and y and how the perimeter is calculated) I'll give general advice.

1. Write the expression for the enclosed area, which will be in terms of x and y.
2. Write the expression for the length of fence used, which will also be in terms of x and y.
3. Since expression #2 is fixed at 100, set the length equal to 100, then rearrange it to get x in terms of y or y in terms of x.
4. Substitute that into the expression #1.
5. You now have a quantity which only depends on one variable. Find the maximum of that function by whatever methods you have been taught.

To be honest, if you do manage to post a picture, none of my advice will change. It will just allow us to help you with the expressions in step #1 and #2 in case you're struggling with that.
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dm me the picture and i'll try to help

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