You were close, but the correct answer to 200 x 40 is 8,000.  We tell students to take all the zeros from the problem and put them in their hand.  That is three zeros, leaving you with 2 x 4.  Multiply that, and you get eight.  Now put the zeros from your hand at the end.  The answer is 8000.

I recommend reading Volume 1 of the Learn Math Fast System.  That book will teach you tricks like the one above that will make math faster and easier to solve.  Older students can complete that book in about one month.  Use the coupon code PT2026 to get 10% off your order.