4-4 point low approach high extension peep
In response to the 4-4 point low approach high extension, the peep at is currently (mid 2024) the most popular reply. This is often thought of as an AI innovation, although it appears in a handful of 20th-century games, going back as far as an Oteai game between Kubomatsu Katsukiyo and Takahashi Shigeyuki in 1930.
The most common reply is the solid connection at a. The kick at b is also reasonably common, and can lead to a very complicated fight. All of c through g have appeared in pro games.
Connect
After , white will usually continue at , and then black will often tenuki. After , the low pincer attack at with at a is an interesting possibility.
White might also tenuki after the - exchange. If so, then black has good follow-up moves at b or c.
If we reverse the order, is inefficient. Black could defend against the threatened push and cut by playing at a instead, or even further away at b. (In fact, KataGo suggests that black can often tenuki after , although it leads to a complicated fight if white plays at later.)
Kick
After , black can also resist with . In this case, and are almost inevitable, then white can choose between a for a peaceful resolution, or b or c to start a complicated fight.
This is just one of many ways the fighting might continue. Notice that this is an exception to the proverb "cut the side you don't want": at would be a mistake. (If white plays at instead, the same applies: white should add a second stone and fight, instead of sacrificing.)