Let $A=\{a,b,c,d\}$ and $B=\{1,2,3,4,5,6\}$. Then the number of one-to-one functions from $A$ to $B$ is:

A one-to-one function maps each element of $A$ to a unique element in $B$.Number of elements in $A$, $n(A)=4$.Number of elements in $B$, $n(B)=6$.The number of one-to-one functions is given by $P(n(B),n(A))$:
$$P(6,4)=\frac{6!}{(6-4)!}=\frac{6!}{2!}=6\times 5\times 4\times 3=360$$