To enhance something is to add to its desirability or to magnify it. To augment something is to make it larger or to increase it. A person might augment or supplement their income by taking a second job; a teacher might augment course curriculum with unique educational experiences. Augment is often used to talk about additions that are made to meet needs, standards, or requirements.
Something that is intricate has many interrelated parts or facets. Such involvement or entanglement can be the source of wonder or appreciation, as in the case of intricate patterns in nature or art, or frustration, as in the case of an argument that is so intricate it is difficult to understand. Networks, webs, and systems are interrelated by definition; in describing complex entities such as these, intricate draws special attention to their elaborate nature.
Posthaste, also spelled post-haste, is an adverb that means “with the greatest possible speed or promptness.” It works in a sentence similar to immediately or ASAP. When the term entered English, it referred to speed like that of someone traveling post, or riding express to deliver mail. Nowadays you can use it to command speedy movement or action, “Leave the premise posthaste!” or to describe it, “She came to her friend’s aid posthaste.”