In Hatchet, how does Brian measure time?

Brian measures time in a couple of ways.  One way is literal.  Brian marks off the days in the wilderness at his shelter door, on stone.  Each mark is a day and in this, Brian is able to fully grasp the length he has been in the wild and also note how time is measured.  In a more symbolic way, Brian marks off time in his own mind as to specific events that he has had to endure.  The struggle for a food source, the discovery of fire, the cultivation of fire, the words of Perpich in taking things in an incremental manner, as well as the need to develop "tough hope" are all examples of this.  As Brian becomes more reflective in the wild, he recognizes that time is measured in how much he has changed.  In this, time can be seen in a subjective manner, something that exists outside the realm of the objective.  In measuring in time through this manner, I think that Brian is able to demonstrate maturation and growth in that he recognizes that he can only control what experiences he has as well as how he appropriates his own setting.  In conceptualizing time in this manner, Brian demonstrates a sense of maturation and growth as he marks off time in his time.

Time is an odd thing for Brian while he's lost in the wilderness. He doesn't have anything like a clock or a watch that would allow him to keep an accurate track of time during the day. Of course, he can generally track morning, noon, afternoon, and night by the movement of celestial objects like the sun and moon. Though he doesn't have a calendar, Brian can keep track of days based on a simple day and night cycle, and he notes each passing day by making a mark on the stone that is near the door to his shelter. Unfortunately, the days blur together so much that the marks on the rock are essentially useless. It's something for him to do, but these marks hold little meaning to Brian.

As time passes, Brian adopts an alternate way of noting the passage of time. This alternate method sees Brian orienting himself around major events, which prove more meaningful to him than the tallies on the wall. Certain events are so traumatic or so crucial to Brian's survival that they are burned into his memory, and he keeps a mental journal of those events. Events like First Meat day and First Arrow day are examples of the way Brian now orients himself around these important occasions. While this method isn't an exact way of measuring the passage of time, it is better suited for Brian's new life, serving as a way for Brian to measure his maturation and growing set of skills. Individual days are typically void of variation, so they don't mean anything to him; however, learning some new survival tactic or skill is hugely important to Brian, so those are the days and times that are most meaningful to him.

What two methods does Brian use to measure time in Hatchet, and which is most meaningful to him?

This question is asking about information that readers can find at the very beginning of chapter 15. Readers are told that the days began to blur into each other for Brian, and keeping track of them was essentially useless; however, Brian does keep track of each passing day by putting a mark in the stone near the door to his shelter. Despite him putting these marks here, they mean next to nothing to Brian, because all a day is to him at this point is a time with light in between dark periods.

Brian learns to use an alternative time-keeping method, and that method prioritizes events. Brian keeps a mental journal of specific events that were burned into his memory because of their importance. These events are things like First Meat day and First Arrow day. These events are so significant to Brian that they are the way he marks "real time." Obviously, keeping track of these events is not exactly a way to keep track of time, but it is a way for Brian to track his maturation process. Days don't mean anything to him because there is hardly any variation in them, but succeeding in some kind of survival tactic is hugely important to Brian, and those days are meaningful because they help build him into a better survivor.