I think that you will need to look at your own book to get whatever your book's author says are the four essential elements of a contract. This is because different authorities hold that there are different elements of a contract that are essential. For example, West's Encyclopedia of Law (see the link) holds that there are seven or eight elements that must go into every contract.
In West's, the elements are as follows:
The requisites for formation of a legal contract are an offer, an acceptance, competent parties who have the legal capacity to contract, lawful subject matter, mutuality of agreement, consideration, mutuality of obligation, and, if required under the STATUTE OF FRAUDS, a writing.
To me, the four most important elements of the contract are the offer, the competent parties, the legal subject matter, and the acceptance. This is because these are the things that define a contract -- a contract must be between people of sound mind and legal age. It must be about something legal in order to be binding. There must be an offer made by one of the parties and agreed to by both.
So, those are my 4 essential elements, but your book may see things differently.
Now that I think of it, I wonder if you might be using Street Law which is a text that I have used when teaching very basic law to high school students. It says the four elements are
- Mutual agreement
- Consideration (you have to give something in exchange for what you are getting)