You are basically using a search filter here.
One of the ways would be to set the autopostback of the checkbox to true. Whenever a user checks a checkbox, the page will be posted back to the server. Get the checkbox id there and find the value against it. Then do a search for the product with the keyword in all the search allowed columns in the database. But I am sure that isn't the best way to do it.
That being said, you will have to be very careful about the design. Search is an important part of any eCommmerce application so you must be very careful about the performance. You may have to use Caching techniques and will have to optimize your SQL query very well (indexing proper columns will be important).
I would suggest you first read more about how it works and some architectural design guidelines before you code it.
The Google search link should help you -
search filter ecommerce asp.net[
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