first of all, I really haven't learn any javascript at all, and I am stuck here.

I want to get these link in this JSON example.
"list": [
[
"List of recipes",
[
{
"name": "Eggs",
"links": [
{
"method": "Fry",
"link": "https://example.com/category/fry"
},
]
},
]
]
I can't elaborate with my friend's example code, can anyone help me?
Your JSON isn't valid so you need to fix that first.
When it's valid parse it with JSON.parse.
When it's parsed you'll have a nested array data structure. You need to access the links array by navigating through the tree with the array indexes.
// Returns an array
data.list[0]
// Get the second element of that array
// (the first element is the text "List of recipes")
// which is also an array
data.list[0][1]
// Access the first element of that array
// (an object) and return the links array
data.list[0][1][0].links
const json = '{"list":[["List of recipes",[{"name":"Eggs","links":[{"method":"Fry","link":"https://example.com/category/fry"}]}]]]}';
const data = JSON.parse(json);
console.log(data.list[0][1][0].links);