Let [tex]x_1,\ldots,x_4[/tex] be the four numbers. Their average is 8, so
[tex]\dfrac{x_1+x_2+x_3+x_4}4=8[/tex]
You know that three of the numbers have a sum of 22, so
[tex]\dfrac{22+x_4}4=8[/tex]
Solve for [tex]x_4[/tex]:
[tex]\dfrac{22+x_4}4=8\implies22+x_4=32\implies x_4=10[/tex]
