The image below is the cover photo of a CD from a famous actor in Japan. Aren’t you making a mistake of believing that this is the correct way of greeting people in Japan? If so, you should stop it immediately! If a Japanese person bows to me with his/her hands together like this, it will make me feel very uneasy because it feels like I am not seen as a real person.
Putting your palms together in front of your chest like this and bowing is a way of praying, not greeting a real living person. If you are giving thanks to an invisible higher being like when you say “itadakimasu” just before eating, that is perfectly fine, but you should avoid doing it when you are face-to-face with somebody.
When Japanese people bow, they have their hands down and tilt their whole upper body keeping their back straight. Your eyes should follow your own movement, i.e. you should NOT be gazing at the other person’s eyes, when your whole upper body is being tilted.
The easiest way of achieving these all is to have your hands below waist and look at your own toes, keeping your back straight. That will give you the right amount of tilt expected in everyday greeting! Do not ever have your hands in front of your upper body!