What's the meaning of this sentence?
Not much I can hand to you this very moment.
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So, it means “there is little I can give you right now”.
A phrase like this might be used by someone who needs to give you bad news but at the same time wants to spare your feelings.
When spoken, it might be said with a sympathetic expression and maybe added emphasis
Not much I can hand to you this moment
...when the truth might be that there is nothing to give you, and there might never be.