The first trick of this exercise is recognizing you don't need to calculate the odd fibonacci numbers.
The series of only the even numbers is :
0, 2, 8, 34, 144, 610, 2584, 10946, 46368, 196418, 832040, 3524578, ...
So starting with 0 and 2 the next element is always 4 times the preceding one plus the one before that :
34 = 8*4 +2
144 = 34*4 + 8
...
Now the exercise is simply caluclating this series and keeping a running total, until you hit 4_000_000. If you do that using primitive long the performance is a lot better than what you have so far.
Output on my PC :
Yours : Result: 4613732. Time used for calculation in nanoseconds: 530009.
Suggested : Result: 46137344613732. Time used for calculation in nanoseconds: 3603.
Edit : when I replaced 4*b + a
by b + b + b + b + a
performance got even better :
Result: 4613732. Time used for calculation in nanoseconds: 1201.