The second line obj[{key:"instagram"}] = "Akrixa"; creates a key within your obj [{key:"instagram}] (which is an object inside an array) and then sets the value of that key to Akrixa, and the third line does the same but with a different key and value.
It might be better to use obj["instagram"] = "Akrixa" and obj["facebook"] = "Coding with Akrixa" as to avoid excessive complication, and you can then refer to it with obj["instagram"] etc.
let obj = {};
obj["instagram"] = "Akrixa";
obj["facebook"] = "Coding with Akrixa";
console.log(obj["instagram"]);