Figure out what's wrong please

To put it simply, the prompt() command is an alert box that allows the user to store input. It appears, based on what you wrote in the question, that you actually wrote your prompts twice. You only need to store them each ONCE to store them in the catch vars you used (user_response, age_declaration).

    console.log("begin the program");
    var user_response;
    user_response = prompt("Hey! welcome to my Website.. Thanks for visiting Please what is your name?");
    alert(user_response);
    var age_declaration;
    age_declaration = prompt("Hey!, How old are you?");
    alert(age_declaration);
    document.write("Your name is " + user_response + " and you are" + age_declaration);
    alert("Thank you for visiting");
    console.log("end of the program");

Use this for reference. This should behave how you want it to. Just remember you only need to declare these prompt() commands ONCE and that ONCE should be where you store the variable, given that you want to record the information.

If you run your code before using what I provided, try recording different names (I.E. Bob then Bill). Bill will get written and Bob will be forgotten. Same thing with applies to age; if you wtie 36 and 13, 36 will get dropped and 36 will be recorded isntead.

Hope this helps.