Half hexagons are actually not hard at all.
The trick is to realize that you can't just divide the hexagon in half, that is, make 3 pairs of 2 cluster stitches, because if you do, you're trying to crochet into side spaces that don't exist.
See where the pen is pointing in the picture above? When you make a half hexagon, the spaces between clusters are what you're trying to create, because that's what you're crocheting into on each round. If that still seems a little mind boggling, then just follow the pattern below, and it will make more sense.
I adapted the hexagon pattern from One Loop Short, and here's what I did:
Half Hexagon Recipe
Special stitches Cl St = Cluster Stitch: YO and
pull a loop through ring, YO and pull through 2 loops on hook (3
times), YO and pull through all 4 loops on hook.
1. Ch. 5 and join with a sl. stitch to form a ring.
2. Ch. 3, dc in ring, *(Ch2, yo and pull a loop
through, [3 loops on hook], yo and pull through 2 loops [2 loops on
hook], yo and pull a loop through [4 loops on hook], yo and pull through
2 loops [3 loops on hook], yo and pull through all 3 loops on hook), repeat from * once more, then ch. 3 and dc into ring. End color.
3. Join new color, Ch. 3, dc into the first cluster, ch2, (yo and pull a loop through, yo and pull through 2 loops) twice, yo
and pull through all 3 loops, ch2, cl st in same space, ch2, work two cluster stitches in the next ch. 2 space, ch. 2, work one cluster in next space, then ch.3 and dc into the same space.
4. Join new color, Ch. 3, work 2 dc in same space. *(Work 3 dc in next space. In next space, work 3 dc, ch. 2, 3 dc). Repeat from * once more, then 3dc in next space, 3 dc in last space.
Finish off and weave in all those dangly ends.
If you try this and find a problem, please let me know in the comments and I'll correct the pattern. Hopefully it's okay, though.
Oh, and here's a picture of the finished afghan.
Now all I need is a border. (*Sigh*) It's always something, isn't it?