How to write this Lisp / Scheme code?

Applying the function to twice the number:

(lambda (f x) (f (* 2 x)))

Applying the function to the number twice (which is what you may have intended to ask):

(lambda (f x) (f (f x)))

Greg's answer is correct, but you might think about how you might break apart this problem to find the answer yourself. Here is one approach:

; A lambda expression
;(lambda () )

; which takes a function (of one argument) and a number
;(lambda (fun num) )

; and applies the function
;(lambda (fun num) (fun num))

; to twice the number
;(lambda (fun num) (fun (* 2 num)))

((lambda (fun num) (fun (* 2 num))) + 12)

Here is another way to approach it:

Write a Contract, Purpose, and Header:

;; apply-double : function -> number -> any
;; to apply a given function to double a given number
(define (apply-double fun num) ...)

Write some Tests:

(= (apply-double identity 10) 20)
(= (apply-double - 15) -30)
(= (apply-double / 7) 1/14)

Define the function:

(define (apply-double fun num) 
  (fun (* 2 num)))

This is an abbreviation of the recipe here: http://www.htdp.org/2003-09-26/Book/