It is a very polite and emphatic way of saying that I truly appreciate something, that you will never know how much I appreciate it. I am so very thankful . "I can't begin to" is used in other situations as well: I can't begin to understand why you said that; I can't begin to forgive you for what you did; I can't begin to describe how beautiful that scene was; I can't begin to believe that she is dead.
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