The solution is simply the throw-in at followed by making an eye at . The result is, the group with an eye wins the capturing race  since there is no way for White to make approach moves to Black's group.
 Gronk: Warning! While it may be a proverb, it is not without exceptions. (Is it really a good idea to repeat such proverbs, thereby providing incorrect information to players who don't know better? The page would be quite fine without it.)
unkx80: The way I see it is that proverbs give some heuristics for problems. Not exact, but useful nonetheless. Maybe the wording can be improved?
Gronk: In some cases I agree with you (unkx80). But the proverbs I find useful apply to situations in which exact evaluation is extremely hard (typically for the opening, like "urgent point before big point"). For capture races, making an eye can be deadly and exact evaluation is not hard if you have learned the short cuts. So, I don't like this proverb. It just isn't that helpful. A better one would be "An eye (when your opponent lacks one) gives you internal liberties". At least that way it is clear that if there are none (or not enough) internal liberties, an eye is not so useful. Even still, there is no substitute for just learning the counting shortcuts.