Final answer:
Adam's reinstated health insurance policy would typically become effective on the date his reinstatement application is accepted by the insurer or when he has met all the requirements, which include paying past due premiums and any applicable fees.
Step-by-step explanation:
When Adam fails to pay his premium for his health insurance policy by the end of the grace period and the policy lapses, he has to go through the reinstatement process which involves submitting a new application to the insurance company. The specific time frame when the policy will be reinstated after acceptance varies based on the insurer's policies and procedures. However, generally, if Adam's application is accepted by the insurance company, the reinstatement of his health insurance policy could be effective from the date of acceptance or the date when he completes all necessary reinstatement requirements, including payment of all past due premiums and possibly a reinstatement fee.