The correct answer is D) The installation of a siphon tube (pig-tail) oriented vertically in the entrance to the gauge. This is the correct answer because a vertical siphon tube protects the steam pressure gauge from damage by preventing direct contact between the gauge and the hot steam. The vertical orientation of the siphon tube allows condensate to accumulate in the tube, creating a water seal that prevents the steam from reaching the gauge. This helps to dampen the pressure fluctuations and thermal expansion, which can otherwise damage the sensitive components of the gauge. The other options are incorrect because a damping needle valve (A) does not provide the same level of protection as a siphon tube, thermal insulation (C) does not prevent direct contact between the steam and the gauge, and a horizontal siphon tube (B) would not effectively create a water seal to protect the gauge.