These expressions are often confused.
When you have something in your hand, you are holding it.
Have you got anything in your hand?
You are hiding something in your hand, aren’t you?
The expressions ‘at hand’ and ‘in hand’ have literal meanings.
To have something at hand is to have it conveniently near you.
I always keep a dictionary at hand.
When you are working in the kitchen, you must have a fire extinguisher at hand.
When you have small children in the house, you must have a first aid box at hand.
The expression ‘to hand’ has a very similar meaning.
‘Do you remember how many books we sold last week?’ ‘I’m afraid, I don’t have that information to hand.’ (OR … I don’t have that information at hand.)
In hand
The phrase ‘in hand’ has several uses. To have something in your hand is to have an extra amount of something. This expression is commonly used to talk about time.
I will have no difficulty finishing this project before the deadline as I still have three weeks in hand.
A problem / situation in hand is a problem / situation that you are dealing with at the moment.
I have got quite a few problems in hand.
I have got several offers in hand.
To take the situation in hand is to control it.
The police couldn’t take the situation in hand.
If something is in hand, it is immediately available.
We have got thousands of applications in hand.
If something goes out of hand, it becomes uncontrollable.
Unemployment has gotten out of hand.
On / upon your hands
When you have something on/upon your hands, you have it in possession as an added responsibility.
They have four babies and six dogs on their hands.