Converting from base $x$ to base $y$ I'm trying to convert from base $x$ to base $y$, but am having trouble understanding why the following method only works when converting to base $10$.
Take for instance the number $2132$ (base $4$). I can convert it to base $10$ the following way:
$2*4^3 + 1*4^2 + 3*4^1 + 2*4^0 = 158$
So that means $2132$ (base $4$) = $158$ (base $10$).
Now what if I want to convert the same number, $2132$ (base $4$) to base $6$? Why can't I do the same method? Example:
$2*4^3 + 1*4^2 + 3*4^1 + 2*4^0 = 158$
Why is this method specific to base $10$ only?
I know that I can use a different method to convert from base $4$ to base $6$, but I'm not sure why base $10$ has this method that no other base can use?


Take for instance the number $2132$ (base $4$). I can convert it to
  base $10$ the following way:
$2*4^3 + 1*4^2 + 3*4^1 + 2*4^0 = 158$
So that means $2132$ (base $4$) = $158$ (base $10$).
Now what if I want to convert the same number, $2132$ (base $4$) to
  base $6$? Why can't I do the same method? Example: $2*4^3 + 1*4^2 +
 3*4^1 + 2*4^0 = 158$
Why is this method specific to base $10$ only?

Because the basic mathematics for arithmetic you have learned in school (addition table, multiplication table etc.) is the maths for base $10$.
E.g. $3 \cdot 4^1 = 3 \cdot 4 = (12)_{10} = (C)_{16} = (1100)_2$ etc.
Your method is not general purpose, it is only valid to convert to a base $10$ (decimal) representation.
