How does the scope of this private method work?

My question is: how can I see the Tuple result in the process method if it was created in the check method? How am I able to use it there, if it was created in a private method?

 public class Problem13 {
	private Tuple<Integer> costs;

	private Tuple<String> names;

	private Tuple<Integer> result;

	private int budget;

	private int minDelta, minCost, totalCost;

	public void process(String fileName) {
		if (!read(fileName))
			return;

		if (budget >= totalCost) {
			System.out.println("You can buy all items");

			return;
		}

		if (budget < minCost) {
			System.out.println("You cannot buy items");

			return;
		}

		minDelta = -1;

		int n = costs.getLength();

		Set<Integer> interval = new IntegerInterval(0, n - 1);

		for (int k = n - 1; k > 0; --k) {
			Combinations<Integer> combinations = new Combinations<Integer>(interval, k);

			combinations.produce((tuple) -> !check(tuple));

			if (minDelta == 0)
				break;
		}

		if (result == null)
			System.out.println("No solution found");
		else {
			int k = result.getLength();

			for (int j = 0; j < k; ++j)
				System.out.printf("%s ", names.get(result.get(j)));

			System.out.printf("(%d)\n", minDelta);
		}
	}

	public static void main(String[] args) {
		new Problem13().process("data/input13.txt");
	}

	private boolean check(Tuple<Integer> tuple) {
		int k = tuple.getLength();

		int currentCost = 0;

		for (int i = 0; i < k; ++i) {
			int j = tuple.get(i);

			currentCost += costs.get(j);

			if (currentCost > budget)
				return false;
		}

		int d = budget - currentCost;

		if (minDelta < 0 || d < minDelta) {
			minDelta = d;

			result = new ArrayTuple<>(k);

			for (int i = 0; i < k; ++i)
				result.set(i, tuple.get(i));
		}

		return minDelta == 0;
	}

private means private to the class. So Problem13 can see anything defined in that class, whether private, public, protected or package private.

Also, the access modifier of the method only affects who can call it, not where the results can be seen. For instance, if result was defined as a public field, any class (not just Problem13) could see it.

You can find many good breakdowns of access modifiers out there on the Interwebs. Here's one.