PROVE THAT THE TENS DIGIT 3^X IS AN EVEN NUMBER ?

Use induction.

It is true for n =1,2,3 etc.

Suppose it is true for n = k i.e. 3^k has its tens digit even. 3^k+1 = 3. 3^k. The last digit of 3^k is 1 or 3 or 7 or 9. If the last digit is 1 or 3, there is no carry over from multiplying by 3, so that the tens digit remains even. If the last digit is 7 or 3, the carry is 2, so again the tens digit is still even.