When you become fully present, thoughts stop and your mind is silent. You are not trying to stop the thoughts. It simply happens as you become present.
The very effort to stop thoughts is a reinforcement of the thinking process. All you can do is relax, notice that you are in the mind, and then bring yourself present with that which is already present. If you can see it, hear it, feel it, taste it, touch it or smell it, in this moment, then it is of the present moment.
When you are present with something here in this moment, you are not thinking it into existence. It is actually here, now. Thoughts will stop, and you will experience a deep feeling of peace as your mind falls silent.
But there is an even deeper level of peace and silence waiting to emerge, as you become more and more present. As your mind becomes more silent, an inner door is opened, allowing an infinite and eternal silence to emerge.
This infinite and eternal silence is the very essence of your Being. It is your true nature. It is the essence of all existence. It is the eternal silent presence of pure consciousness. It is the "I AM" of you. It is that dimension of you that exists in this moment and only this moment. It is that dimension of you that exists in Oneness.
It is your Buddha nature. It is the Christ of you, which exists in Oneness with God. It is awakened man. It is awakened woman.