Concept:
In an internal combustion engine, valves must open and close at the correct time for proper intake and exhaust operations.
Step 1: The inlet valve allows air-fuel mixture or air to enter the cylinder.
Step 2: The exhaust valve allows burnt gases to leave the cylinder.
Step 3: The camshaft has cams which convert rotary motion into lifting motion of valves.
Step 4: As the camshaft rotates, it raises and lowers the inlet and exhaust valves at the required time.
Step 5: Hence, the shaft responsible for valve operation is the camshaft.
\[
\boxed{\text{Camshaft}}
\]