To attach two spaghetti strands securely without breaking or bending, the discussion emphasizes the importance of configuration, specifically end-to-end and side-by-side placements. For the end-to-end connection, overlapping the strands is crucial to ensure sufficient surface contact. A suggested technique involves pinning the spaghetti to a foam base covered with wax paper to prevent sticking, using angled pins to hold the strands straight while the glue dries. Concerns about the spaghetti leaning after gluing can be mitigated by ensuring the fixture holds the strands gently, avoiding excessive force. The type of glue used is also significant; water-based glues may distort the spaghetti, so a strong super glue is recommended. Proper preparation of the ends of the spaghetti, ensuring they are flat and square, is essential for a strong bond. The conversation concludes with a suggestion to stagger side-by-side attachments for added strength and stability.