This is a fairly simple, but extremely important problem. At first glance, White seems to have a lot of reasonable choices. Here’s a quick list, with a brief description of why each play might be appealing:
(a) 24/18, making the enemy bar-point and duplicating fours, but not making any progress on the front game.
(b) 8/4 6/4, making the 4-point, but leaving two blots and a lot of shots.
(c) 13/9 18/16, making the 9-point and creating some duplication of fours.
(d) 9/5* 18/16, fighting for the 5-point while taking away Black’s good sixes.
(e) 9/5* 13/11, fighting for the 5-point and fearlessly bringing down another builder, but leaving Black with 6s, 5s, 4s, 3s, and 1s to hit.

Seeing the right play hinges on understanding two key principles of early game play:
(1) A permanent strong asset trumps a lot of aggression and flexibility.
(2) A defensive anchor on your opponent’s bar point is very powerful.

If it’s not now obvious, the right play is 24/18. White builds a great asset, the defensive anchor on the 18-point. He also leaves Black with minimal threats, the duplicated fours to make either the 20-point or hit White’s blot.

In general, permanent assets are better than loose hits in the early game. Loose hitting often evaporates into no advantage at all, whereas a permanent asset is a plus for the rest of the game. Beginners and intermediates tend to have trouble with these plays, mostly because they’re ambivalent about the value of the enemy bar-point. Since it’s not an inner point, it doesn’t seem to offer the security of an anchor on the 20-point. And everyone can remember games where you held onto the 18-point too long and were forced off it at an inopportune time.

Put those two factors together and many players downgrade the 18-point, looking for something else to do with their checkers. This, however, is a pretty big mistake. Once you split to the opposing bar-point, your game plan is to make it as soon as possible. Loose hits like 9/5* 13/11 or 9/5* 18/16 are just distractions from the thematic idea.

The second-best play in the position is to grab the other permanent asset with 8/4 6/4. It’s not a bad play, since it makes a good point and smooths out White’s distribution. However, it leaves White more exposed with more blots and no anchor, and so is slightly inferior to 24/18.
If you’re playing well, you should find yourself in a lot of games where you make your opponent’s bar point early. There are problems that can come from sitting on the bar-point, but they’re problems you want to have. Learn to play these positions well and your results will improve dramatically.

Solution: 24/18