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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?

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

In any event you need to start by what you tried to far.
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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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