Demi-bride - db
Half double crochet - hdc
To make a half double crochet.
Yarn over and insert your hook under the stitch.

Yarn over again and pass it under the stitch but not under the 2 loops on the hook (red cross). You have 3 loops on your hook.

Make a final yarn over and pass it under the 3 loops on your hook.

All that's left is a loop on your hook.

You've made a half double crochet!