At a turning point, the kinetic ledger is zero. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
At the turning point, velocity is zero
The position equals the amplitude, so all 16 joules are in the spring ledger.
x=A=4m⇒U=16J
Kinetic energy is zero at the endpoint
The checked kinetic entry is 0, not an inferred caption.