The state of great well-being or happiness can be referred to as:

Euphoria is the state of great well-being or intense happiness, often characterized by feelings of excitement, bliss, or elation. It is a term commonly used in psychology and everyday language to describe an elevated mood state that can be caused by various factors, such as positive life events or the release of certain chemicals in the brain.

The other terms provided do not align with the definition of a state of great happiness. Exacerbate refers to making a situation worse, extol means to praise something highly, and facetious involves treating serious issues with deliberately inappropriate humor. Therefore, euphoria is the most fitting choice for describing an extreme level of happiness or well-being.