Contact the company that made the engineered wood on your floors if you have this information. They can likely sell you a matching piece.
Talk with the contractor who installed the floors or the previous owners of your home if you do not know who manufactured the engineered wood on your floor. Then, contact the company.
Purchase a few different samples if you cannot find the exact type of engineered wood from which your floor is made. Compare the samples to your existing floor. Pay close attention to the color, grain pattern and texture of your floor and the sample. Look at the samples again when the light changes to ensure the closest match possible.