With the rapid development of technologies such as vision–language modeling, sharing images with corresponding descriptions has become a common means of information transfer. Studying data-hiding techniques for JPEG images can protect sensitive descriptions, such as personal information associated with them while sharing images. Therefore, research on data-hiding techniques for JPEG images is of significant importance. However, existing methods that modify discrete cosine transform (DCT) coefficients still have room for improvement in increasing their embedding capacity while minimizing file size expansion. To address this issue, this paper proposes a knowledge encapsulation method for JPEG images using a special hexagonal tessellation matrix. First, a special hexagonal tessellation matrix is constructed based on the characteristics of non-zero AC coefficients. Then, non-zero AC coefficients in JPEG images are paired to form coordinate pairs, and the data are embedded by modifying the non-zero AC coefficient pairs into the coordinates corresponding to the secret data. Experimental results demonstrate that, compared to the previously proposed JPEG image data-hiding schemes, the proposed approach achieves a higher embedding capacity, a minimal file size increase (FSI), and an acceptable peak signal-to-noise ratio (PSNR).