Most beginners have problems playing the two hole draw note on the harmonica. Some believe the problem is with their instrument. This is almost never the case. The problem is your technique. The good news is that you will master the two hole draw, with practice and a little guidance. It is the most powerful note on the harmonica.
Firstly, why the problem with this hole more than the others? The reason is the greater difference between the two hole blow and the two hole draw notes, compared to most other holes (e.g. holes 1, 4, 5 ,6). This causes many beginners to "bend" down the two hole draw note, without meaning to. Later on you will want to bend this note, for now the aim is to play it cleanly.
To get a good two hole draw you need the correct mouth shape or "embrochure". For now we use the pucker or lip block method to get this note. Lower your bottom jaw a little, relax you lips, then push the harmonica a little further into your mouth than you have been doing so far. Now try the two hole draw. Any better?
Try the same exercise again, this time in front of a mirror. Take the harmonica away from your lips, and look at your mouth shape. It should be like the picture below:
Notice that the hole made by the lips is fairly large. Now look at a harmonica hole. If you include the wood (or plastic) edges of the hole you will see that they are about the same size as the one in the photo. This larger hole with your lips allows a better two hole draw note.
The two hole draw will also sound better with a stronger air flow. Try breathing in so that the air fills the top of your chest. Do this several times and remember the feeling. You don't want this kind of air flow. Now try another long deep breath, which fills a large space at the top of your stomach. Keep your back and shoulders straight and relaxed. Repeat this long long breath several times. Now place the harmonica into your mouth, with the lip shape described above, and try another 2 hole draw with this long deep breath. Any better?
You may find that the two hole draw note is still bending down a little. To get a clear note, without bending, it is important that your tongue lies flat on the bottom of your mouth. Place the tip of your tongue on to your bottom teeth, then relax your tongue completely, so that it lies flat. Now try the two hole draw again, with the lip shape and long deep breath described above.
The combination of relaxed lips with the harmonica deeper into your mouth, long deep breath from your stomach and relaxed tongue lying flat in your mouth should help greatly with the two hole draw. Practice these three aspects for 15 minutes each day for a week. The result should be a much better two hole draw note.
Finally, a great suggestion from the Dutch master player, teacher and harmonica customiser Ben Bouman.
"...This is what I tell my students who are having problems with 2 draw.
Sit down on your couch, lean your head backwards supported by the edge of the couch. This will open and relax your throat. Now play the 2 draw , not too loud!
When you now get a clear note, slowly bring back your head forward and try to feel what happens in your throat when the note doesn't sound clear anymore.
This works for almost anyone so I hope this will help you as well.