Prove by induction:
6*7^(n power) - 2*3^(n power) is divisible by 4, for all n is great than or equal to 1
I assume you meant that the expression in the parentheses is even! since $\displaystyle 3*7^n$ and $\displaystyle 3^n$ are odd numbers, and subtracting two odd numbers gives an even number.
To solve by induction, simply follow the steps provided in the other topics you posted..