Which of the following credits are the Lincolns eligible to claim on their tax return?

The Lincolns are eligible to claim the credit for other dependents and the American opportunity credit based on their circumstances. The credit for other dependents allows taxpayers to claim a non-refundable credit for dependents who do not qualify for the child tax credit. This can apply to dependents who are older than 17 or other qualifying relatives, thus allowing the Lincolns to benefit from this credit.

The American Opportunity credit is a valuable educational credit that provides financial relief for qualified higher education expenses for a minimum of four years of post-secondary education. The Lincolns can claim this credit if they have qualifying education expenses for a student enrolled in an eligible educational institution.

While the child tax credit is commonly sought after, it is not made available to them in this scenario due to various eligibility factors, such as income limits or the age of the qualifying child. Thus, the selection of only the credit for other dependents and the American opportunity credit reflects their actual eligibility.