The correct answer is: C. 4.6 A, 6.9 A
The current in each branch is inversely proportional to the resistance of the branch. Therefore, the current in the 8 ohm branch is 6.4 A / 8 ohms = 0.8 A, and the current in the 12 ohm branch is 6.4 A / 12 ohms = 0.5 A.
Option A is incorrect because the current in the 8 ohm branch is 6.9 A, not 6.4 A.
Option B is incorrect because the current in the 8 ohm branch is 6.4 A, not 9.6 A.
Option D is incorrect because the current in the 12 ohm branch is 0.5 A, not 9.6 A.