Is this valid notation?
$$\left\{(a,b) \in \mathbb{R}^2 \;\middle|\; \left(a=6+|b|, |b|\le4\right) \ \text { or } \ \left(|a|\le3, |b|=2\right) \right\}$$How to graph it, please? thanks
It's the result of a problem, but I'm not sure this is a correct way to write it or how to graph the set.
The way you have written is fine, but it's probably nicer to write it as $$\{ (x,y) \ | \ y \in [-4,4], |x| + |y| = 6 \} \cup \ \big( \ [-3,3] \times \{ -2,2 \} \ \big).$$
You can see here (thanks to @mfl) what the first set in the union looks like. The second is just two horizontal lines.
If you lay these on top of each other, then you get what you're looking for.