This was borrowed from the thepokerbank.com's explanation. It seems to get to the ease of the rules intention.

The rule of 4 and 2 is a quick shortcut for helping you to work out the percentage

odds of completing a draw in Hold’em. To get your percentage odds:

Multiply your outs by 2 when you are on the flop waiting for the turn.

Multiply your outs by 2 when you are on the turn waiting for the river.

Multiply your outs by 4 when you are on the flop waiting for the river (opponent is all-in).

When you have multiplied your outs by either 4 or 2, you will get a percentage that you can compare with your

pot odds to work out whether or not it’s worth calling with a drawing hand.

The rule of 4 and 2 just works for percentages odds, not for ratio odds I'm afraid.

Examples of the 2/4 rule.

Flush draw: 9 outs * 2 = 18%

Straight draw: 8 outs * 2 = 16%

Two overcards: 6 outs * 2 = 12%

Two pair and you need to make a full house: 4 outs * 2 = 8%

Flush draw, opponent is all in on flop: 9 outs * 4 = 36%

Straight draw, opponent is all in on flop: 8 outs * 4 = 32%