A second splitter acts only on the arm that actually enters it. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Only one selected arm enters the next splitter
The first splitter sends 8 photons to 4 upper and 4 lower.
8→4+4
The selected arm splits again
Sending the selected upper count 4 through a second balanced splitter gives 2 and 2, while the other path still carries 4.