Answer:
When 6b is divided by 12 the remainder is 42 or 6b mod 12=42.
Step-by-step explanation:
We suppose that b is any integer.
If 7 is the remainder left over when b is divided by 12 and we call m to the number given by the integer division [tex]\frac{b}{12}[/tex]
We have that [tex]\frac{b}{12} =m+7[/tex]
If we multiplied this expression by 6 we get a new one to calculate the remainder of [tex]\frac{6b}{12}[/tex]
Then [tex]\frac{6b}{12} =6(m+7)[/tex] ⇒ [tex]\frac{6b}{12} =6m+42[/tex]
No matter what integer b we start with the remainder of [tex]\frac{6b}{12}[/tex] is 42.
