Advancing Youth Enrollment Act This bill amends the Internal Revenue Code to increase the premium assistance tax credits that are available to taxpayers with household members who are 18-34 years old. (The credit is available to eligible individuals and families to subsidize the purchase of health insurance plans on an exchange established under the Patient Protection and Affordable Care Act.) The bill allows increased tax credits for the taxpayers by reducing the maximum percentage of income that the taxpayers are required to pay for health insurance premiums. This percentage is used to calculate the amount of the credit.