Final answer:
The map() method is the correct answer; it executes a function on each array element to create a new array with the returned values, unlike forEach() which does not return a new array.
Step-by-step explanation:
The method that performs an action similar to the forEach() method, but instead calls a function that returns a value to match the contents of an existing array into a new array, is the map() method. Unlike forEach(), which can only be used to execute a function for each element of an array, map() creates a new array with the results of calling a provided function on every element in the calling array.
It's important to note that while map() may seem similar to forEach() in that both iterate over elements, the former does not execute a function arbitrarily but applies a transformation to each item, thereby generating a new array based on the return values from the function.