1. The problem is to convert the number 4 in base 4 to its equivalent in base 10 (decimal). 2. In base notation, the number 4 in base 4 means: $$4_{4}$$. 3. However, digits in base 4 can only be 0 to 3. The digit '4' is invalid in base 4. 4. Therefore, the number 4 base 4 does not represent a valid number. 5. If the user meant digit '10' in base 4 or a different number, please clarify. 6. In conclusion, 4 base 4 is invalid as base 4 digits are from 0 to 3 only.