The National B campaign in the career mode is where you start to get a variety of race types and vehicles. After you get 10 stars in any combination of National B races, the Coffee Break Challenges for this series open up. The first of these is the Eco Challenge Trial 1, where you need to drive as far as possible on a single liter of gas within a time limit. Here's what you need to do.
The car you have for this is the 2012 Nissan GT-R N24 GT. It's a beast, but has everything you need to get past the mileage limit within the time frame.
Eco challenges are different. Normally in racing games you want to go as fast as you can. In the eco challenges, however, you need to focus on proper consumption of fuel combined with knowing how to accelerate properly, when to brake, and when to coast.
At the start, the most important thing is to not gun the accelerator. Simply put - do not floor it off the line. If you do, you'll probably waste over 10% of your gas, and need to hit the brakes right away; this is a perfect recipe for failing to get gold.
Once you're moving, you'll never want to get over 3rd gear. Doing so drains your fuel significantly. You'll also want to avoid using the brakes. Believe it or not, you can get away with this after a few practice runs.
As you wind your way through the track and get closer to the end of the timer, you'll have to play it even smarter. When your fuel game is around .30 liters, gas it for just about .05 liters at a time. Doing this will put you over the mile limit for gold with plenty of time to spare.