Let [tex] x,y [tex] be the two numbers. One number is 6 more than the other, so let's say that [tex] x = y+6 \iff y = x-6 [/tex]
Also, three times the sum of the two number (i.e. [tex] 3(x+y) [/tex]) is equal to 22 more than the larger number (i.e. [tex] 22+x [/tex]). Note that [tex] x [/tex] is the largest, because it is 6 more than [tex] y [/tex].
So, if we set the two expressions to be equal, and we substitute [tex] y = x-6[/tex], we have
[tex] 3(x+y) = 22+x \iff 3(x+x-6) = 22+x \iff 3(2x-6) = 22+x \iff 6x-18=22+x \iff 5x = 40 \iff x=8 [/tex]
And since [tex] x [/tex] is 6 more than [tex] y [/tex], we have [tex] y=2 [/tex]
