Metamer is another way to say the term isomer. Two chemical compounds are isomers of each other if they have the same type and number of each element as each other but they vary by the bond connectivity of the atoms in three dimensional space. To change from one isomer to another would require chemical bonds to be broken and reformed.
We are looking at the number of isomers for EtC4H10O. The Et stands for the ethyl group. Since there are 10 hydrogens and only 4 carbons, we know that each carbon must be fully saturated to accommodate these parameters. In other words, there are no double or triple bonds present. Also, the Et group must be located either between two carbon atoms or between a carbon and the oxygen atom. When we draw out the different possibilities we find that there are 8 different isomers for EtC4H10O. The structures are drawn out below:
Any other structure would be able to be flipped around or otherwise manipulated to one of the above structures without breaking any chemical bonds. So the answer is 8.