what is 6 x 9 in base 13 ?

Because 54 in base 10 is 42 in base 13. 4*13+2 = 54. So it checks out.

54 = 4*(13^1) + 2*(13^0) = 42 in base 13.

But it does matter what base it is in. It's not 42 in base 10.

It's not 42 in base 11 either:

54 = 4*(11^1) + 10*(11^0) = 4T in base 11.

the most common base we use is decimal or base 10.

In this case 6 x 9 = 54 in decimal; if we devide by 10, the result would be 5 and 4 as remainder...

In base 13, we need to devide that 54 by 13; the result would be 4 and 2 as remainder...

13 x 4 = 52

54 - 52 = 2

thus the result is 42.

have you ever wondered why the digits we have in our number system are 0,1,2,3,4,5,6,7,8,9? What would happen if we only had 6 digits? Then counting would go 0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, ... 51, 52, 53, 54, 55, 100, 101, 102, ...

What if we had 13 digits? 0,1,2,3,4,5,6,7,8,9,@,#,$

Then counting would go a little differently. you have things like 2*5=@, 3*4=$, 2*7 = 11, etc. However, if you took "11" pennys (I say 11 in this 13 digit number system), and then counted the pennys in the normal way, there would be 14 of them.

If you multiply 6x9 in this weird way, you get 42. However if you spread out "42" pennys and counted them in th normal way, you would get 54.