Do I need J2SE Development Kit Update and J2SE Runtime Environment update 6 at the same time in my computer? Can I uninstall any of them without causing troubles?
Yes, you can uninstall one of them without causing troubles. From what it seems J2SE Runtime Environment is an older version of J2SE Development Kit and you can safely remove it. In order to uninstall the utility from your computer, I suggest you use Java Uninstall Tool. This application detects all Java versions from your computer and removes those that are outdated.
