# for your blood, the life that is in your blood

"if anyone causes your blood to pour out" or "if anyone spills your blood" or "if anyone kills you" 

# life

This refers to physical life.

# I will require payment

"I will require anyone who kills you to pay"

# From the hand of every animal I will require it

"I will require any animal that takes your life to pay"

# From the hand of any man, that is, from the hand of one who has murdered his brother, I will require an accounting for the life of that man

"I will require anyone who takes the life of another person to pay"

# From the hand of

"From that very man" 

# brother

Here "brother" is used as a general reference to relatives, such as members of the same tribe, clan, or people group.