6.
[tex]\it \overline{a,b}+\overline{b,a}=12,1|_{\cdot10} \Rightarrow \overline{ab}+\overline{ba}=121 \Rightarrow 10a+b+10b+a=121 \Rightarrow \\ \\ \Rightarrow 11a+11b=121|_{:11} \Rightarrow a+b=11=2+9=3+8=4+7=5+6=\\ \\ =6+5=7+4=8+3=9+2\\ \\ (a,\ b)=\{(2,\ 9),\ (3,\ 8),\ (4,\ 7),\ (5,\ 6),\ (6,\ 5),\ (7,\ 4),\ (8,\ 3),\ (9,\ 2)\}[/tex]
