How do you say can you read this in Japanese?

読めますか (yomemasuka) translates literally as "can read?" In order to best articulate the question it would be better to ask if one could read "this book" or "this magazine" in which case, you would say この本を読めますか (kono hon wo yomemasuka) and この雑誌をよめますか (kono zasshi wo yomemasuka) respectively. However, should you not know what to call an object, gesturing and context would likely get the point across.