Can you substitute a half double crochet for a double crochet?

For a double crochet, you yarn over and pull a loop through the target stitch. There are three loops on the hook, the one you started with, the yarn over, and the loop you just pulled up though the target stitch. Pulling a loop through two loops at a time means two strokes, or a double crochet. A treble builds on this.

For a treble crochet, you yarn over twice before pulling a loop through the target stitch. That means four loops on the hook. Pulling a loop through two loops at a time means three strokes, or a treble (triple) crochet. A double treble builds on this.

For a double treble crochet, you yarn over three times before pulling a loop through the target stitch for a total of five loops on hook. Pull a new loop through two loops on the hook four times.

To put it another way: The procedure is to yarn over three times, insert hook into the indicated stitch, yarn over and pull through the stitch (5 loops on hook at this point), yarn over and pull through two loops at a time, four times.

Just as in the double and treble above you increase the number of beginning yarn overs and the number of times you pull through two loops.

It seems like it ought to mean 2 x 3 or six loops, but it doesn't. A triple treble isn't 3 x 3 either, it's four yarnovers and five loops.

The abbreviation for a double treble is typically dtr.