Don’t put semicolons after if () or else if () or else.
else is used for when anything specified by if () or else if() is not the case, you don’t put brackets
after an else, in your case you should use an else if (), with that one it works.
Here’s your debugged code:
var December = prompt("What’s today?");
if (December === "24 days until christmas") {
prompt("Today is " + December);
} else if (December === "wrong") {
prompt("That is " + December);
}