Sharing on a desert island

Relevant wiki: Distinct Objects into Distinct Bins

There are $6$ distinct objects being distributed into $2$ distinct bins. The number of distributions of this type is $2^6=64$ .

However, it is specified that each person will receive at least one object.

There is $1$ distribution in which Sri gets all the objects. Likewise there is $1$ distribution in which Godfrey gets all the objects. Therefore, the number of distributions in which each person gets at least one object is $64-1-1=\boxed{62}$ .

IF you've watched distinct balls into identical bins; Just S(n,r) will give you the value of n objects into r identical bins(non empty). Now just permute r boxes and you get answer for distinct into distinct. So, answer is :
2! S(6,2) = 2 x 31 = 62

Total distributions=2^6=64. There are two cases when each gets all the items. So answer is 64-2=62.