If programmers of functional languages were better at naming things, it would be easy. Let's rename g to callTwice and h to aFunction:

  function callTwice(aFunction) {

    return function(y) {
      return aFunction(aFunction(y));
    };

  }

  function square(x) { return x*x; }

  var squareTwice = callTwice(square);

  81 === squareTwice(3);