Having heard both of these idioms I would like to know if they have the same meaning?
- I know something/somebody like the back of my hand.
- I know something/somebody like the palm of my hand.
Having heard both of these idioms I would like to know if they have the same meaning?
There is an idiom - to know something like the back of one's hand, meaning to be very familiar with that thing. There is no widely used idiom involving knowing something like the palm of one's hand.
Both are in use, but I've always heard "like the back of (one's) hand". According to COCA, this form is many times more popular than the version with "palm" (maybe as much as 20 times). Therefore I would highly recommend using "like the back of (one's) hand".
Examples:
I remember our house in Mount Vernon like the back of my hand. It was like a fairy tale. —What Happened, Miss Simone?
We're still talking about my son. I know you like the palm of my hand. And I know there is nothing you would not do for your son. —Caged Animal