Quran says: {And We have enjoined upon man [care] for his parents. His mother carried him, [increasing her] in weakness upon weakness, and his weaning is in two years. Be grateful to Me and to your parents; to Me is the [final] destination.} [Quran 31:14]
My Question is: Should this gratitude be shown loudly in words OR silently in heart?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Gratitude to the parents should be with the heart, tongue and limbs. As-Sa’di interpreted this verse by saying: “…this is by being kind to them with nice and soft words, and by good actions, and by being humble to them, respecting them and honoring them. Also, by fulfilling their needs and avoiding mistreating them in any way, either by words or actions."

Allah Knows best.