When using a 3x Barlow lens with a tabletop Dobsonian telescope, you might encounter issues where you cannot achieve enough inward focus, meaning the focus plane of the telescope does not reach far enough into the housing to create a sharp image. This issue often arises in small tabletop Dobsonians because of their compact design, which can limit the range of focus travel.

Here are several approaches to address this issue:
Check Eyepiece Compatibility: Ensure that the eyepiece you’re using with the Barlow lens is compatible. Some eyepieces, especially longer focal length ones, might require more inward focus than what is available.
Adjust the Primary Mirror: For telescopes with adjustable primary mirrors, you can try moving the primary mirror forward slightly. This adjustment brings the focal plane closer to the eyepiece.
Use a Focuser Extension Tube: If inward focus is insufficient, a focuser extension tube can temporarily add additional outward focus distance, allowing the scope to reach an appropriate focus point at the expense of losing inward focus. Use this carefully, as it might not aid with inward focus but can test where your current focus limitations lie.
Remove the Barlow Lens Temporarily: Test focusing without the Barlow lens to see if you achieve a sharp image. If the problem only occurs with the Barlow lens, then the issue is likely with the lens-to-eyepiece combination.
Investigate Different Barlow Lenses: Different models and brands of Barlow lenses have varying optical designs, which can affect focus length requirements. Trying a barlow lens with a shorter optical path might solve the problem.
Upgrade the Focuser: Consider upgrading to a more sophisticated focusing mechanism if the stock focuser doesn’t provide enough travel.

Understanding and addressing focus issues may require a bit of experimentation and investment. If these methods do not resolve the issue, consult the telescope manufacturer’s support or astronomy forums for additional guidance tailored to your specific model and setup.