Receptor occupancy is the signal divided by signal plus a half-signal constant, so when the signal equals that constant the occupancy is exactly one half. With signal 6 and half-signal constant 6, the denominator is 6 + 6 = 12 and the occupancy is 6/12 = 1/2 exactly for the stated toy binding model; real chemotaxis has receptor noise, ligand diffusion, adaptation, saturation, and measurement uncertainty.
A signal equal to the half-signal constant gives half occupancy. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Signal equals the half-signal constant
The signal is 6 and the half-signal constant is 6.
6+6=12
Signal over signal plus half-signal gives one half