Only one 8 hour period. Any additional travel would require checks to avoid exhaustion
You are asking if a character/party can alternate 8 hours of travel with 8 hours of resting but, unforunately, a character can only benefit from a long rest once per 24 hours:
A character can't benefit from more than one long rest in a 24-hour period, and a character must have at least 1 hit point at the start of the rest to gain its benefits.
This means that the second "chunk" of travel would incur a check to resist suffering levels of exhaustion every hour because, even if the party pulled off the side of the road to "rest", they wouldn't receive the benefit of a long rest:
Forced March. The Travel Pace table assumes that characters travel for 8 hours in day. They can push on beyond that limit, at the risk of exhaustion.
For each additional hour of travel beyond 8 hours, the characters cover the distance shown in the Hour column for their pace, and each character must make a Constitution saving throw at the end of the hour. The DC is 10 + 1 for each hour past 8 hours. On a failed saving throw, a character suffers one level of exhaustion.
Put another way, you can travel as many hours in a day as you want. You get one long rest per day and 8 hours of travel per long rest "for free." Any travel beyond that requires you to make a check each hour to resist exhaustion, regardless of how you break up the travel.