The IUPAC name of a cycloalkane with 9 carbons is cyclo-nonane. To determine the number of stereoisomers for the compound with two methyl groups in a trans-configuration, we need to consider the possible positions of the methyl groups on the cyclo-nonane ring. Let's number the carbons in the ring from 1 to 9. If we place the first methyl group on carbon 1, the second methyl group can be placed on carbons 4, 5, or 6 to maintain a trans-configuration. This gives us three possible isomers:1. 1,4-dimethylcyclo-nonane trans 2. 1,5-dimethylcyclo-nonane trans 3. 1,6-dimethylcyclo-nonane trans Now, if we place the first methyl group on carbon 2, the second methyl group can be placed on carbons 5 or 6 to maintain a trans-configuration. This gives us two more possible isomers:4. 2,5-dimethylcyclo-nonane trans 5. 2,6-dimethylcyclo-nonane trans Finally, if we place the first methyl group on carbon 3, the second methyl group can only be placed on carbon 6 to maintain a trans-configuration. This gives us one more possible isomer:6. 3,6-dimethylcyclo-nonane trans In total, there are 6 stereoisomers of cyclo-nonane with two methyl groups in a trans-configuration.