Back then houses used to be made of straw and mud. Now, houses have been innovated and made out of wood, and are much larger and advanced too.
This is a form of innovation
Diffusion is the spreading of something worldwide. An example is Christianity. Over time, Christianity has spread to everywhere in the world.
When colonists moved to America, they took over the Native Americans. They made them change the Native American's religion to Christianity. This is a form of assimilation because the main culture, which is the colonists, replaced the weaker cultures religion with their own.
Cooking is a very obvious form of acculturation. Most of the food we eat is made from or imported from other cultures or countries. This is a form of acculturation because it is when a culture or something in the culture changes, due to a blending of other cultures and their certain habits or ways of doing things.
Syncretism is when the blending of 2 cultures forms into one thing. it is particularly art, music, or religion. An example of this is tex-mex food. Tex-mex food is a combination of Mexican and American cuisines.