4. In the expression $S=\sqrt{x_{1}-x_{2}+x_{3}-x_{4}}$, $x_{1}, x_{2}, x_{3}, x_{4}$ are a permutation of $1,2,3,4$. The number of different permutations that make $S$ a real number is $\qquad$
4. 16 If $x_{1}, x_{3}$ take 1,4, there are $2 \times 2=4$ permutations; if $x_{1}, x_{3}$ take 2,3, there are $2 \times 2=4$ permutations; if $x_{1}, x_{3}$ take 2,4, there are $2 \times 2=4$ permutations; if $x_{1}, x_{3}$ take 3,4, there are $2 \times 2=4$ permutations. Therefore, the number of different permutations of real numbers in $S$ is $4+4+4+4=16$ (permutations).