Convert number from one radix to another
You're re-inventing the wheel. In the Integer class, there are methods for converting numbers to and from Strings with a radix parameter. So the following class does the job:

package test;

public class Test {

    public static void main(String[] args) {
        int inRadix = Integer.parseInt(args[1]);
        int outRadix = Integer.parseInt(args[2]);
        int value = Integer.parseInt(args[0], inRadix);
        String result = Integer.toString(value, outRadix);
        System.out.printf("%s (%d) = %s (%d)%n", value, inRadix, result, outRadix);
    }
}


But let's for a moment suppose the methods weren't there and look at your solution.

First, the method name convertToDecimal shows a (quite common, I have to say) mis-understanding. An int is internally represented in binary (radix 2), not decimal (radix 10). So convertToInt would be a better name.

I'd extract the character-versus-digit-value logic into methods int digitValueOf(char ch) and char digitCharFor(int digit) (By the way, the Character class has these methods).

I'd replace the numbers like 48 by the characters they represent (e.g. '0'). Not every reader knows the Unicode table by heart.

I'd replace the Math.pow() by consecutive integer multiplication. Turn the loop the other way round, starting from the last digit with placeValue = 1. In every iteration, multiply placeValue by radix. Math.pow() is slower and less exact than integer arithmetic.

I'd get into the habit of adding Javadoc even to trivial methods. After a year or so, you'll be happy.

Personally, I'm lazy with comments inside methods. A good method name, a Javadoc explaining what the method does (not how), and a straightforward implementation within the method are typically enough for a reader to understand what's going on.

Good is the usage of StringBuilder instead of concatenating Strings (quite common performance killer).

Good is throwing an exception in case of illegal characters.

Good is following the standard Java naming conventions.