Origami, the art of folding paper, has been extensively explored for its potential to produce complex structures and enable rapid and precise movements with few folds. The flexibility and low thickness of paper make it ideal for folding, although most engineering applications require stiffer and thicker materials when drawing inspiration from Origami. For that, several techniques have been developed over the years and the double-hinge technique is one of the least explored techniques for thick Origami, even though it shows a major advantage to obtain a fully flat surface in the unfolded state. This advantage makes it ideal when developing solar panels where flat surfaces are required to maximize the absorbed energy. In this work, the Miura Ori pattern, based on the degree-4 vertex coupled with the double-hinge thickness accommodation technique, is analyzed to obtain relationships between the kinematics, thickness, sector angles, and periodicity. It is found that by releasing certain degrees-of-freedom, the double-hinge technique can be used to fold Origami patterns, with flat-foldability and preserving the Origami motion. The findings of this research contribute to a deeper understanding of thickness implications in the double-hinge technique for Origami-based thickness accommodations. This study presents a novel model that has not been previously explored, establishing key insights that are crucial for future emerging applications.