The result follows directly from properties of modular arithmetic:
[tex]b\equiv5\pmod{12}\implies 7b\equiv35\equiv-1\equiv\boxed{11}\pmod{12}[/tex]
That is,
[tex]b\equiv5\pmod{12}[/tex]
means we can write [tex]b=12n+5[/tex] for some integer [tex]n[/tex]. Then
[tex]7b=7(12n+5)=12(7n)+35[/tex]
and taken mod 12, the first term goes away, so
[tex]7b\equiv35\pmod{12}[/tex]
etc
