The BeiDou-3 Global Navigation Satellite System ( BDS-3) can provide data of six frequencies at present, which provides more choices for Multi-frequency Carrier Ambiguity Resolution (MCAR). Focusing on BDS-3, the basic method of Geometry and Ionosphere Free (GIF) model in MCAR is comprehensively studied, including the application of three-frequency GIF model in ambiguity resolution. Based on the theory of three-frequency linear combinations, the basic mathematical model under three-frequency is given. The optimal frequency combination for ambiguity resolution using GIF model is discussed under the possibility of 20 combinations of any three of the six frequencies. Meanwhile, the optimal linear combination of each frequency combination is also systematically discussed. In addition, the high-quality linear combinations for single-epoch ambiguity resolution using GIF model are also analyzed. The experiment is carried out by using the real BDS-3 six-frequency data. Through theoretical analysis and practical demonstration, the results show that when using the GIF model for ambiguity resolution, the optimal frequency combination is (B1C, B3I, B2a). In this method, if the sum of the coefficients of two fixed Extra Wide Lane /Wide Lane (EWL/WL) combinations equals zero, the standard deviation of the ambiguity for the third Narrow Lane (NL) combination is theoretically dependent solely on the frequency characteristics. However, due to the influence of unmodeled errors, the actual results may deviate from theoretical expectations. The GIF model effectively eliminates ionospheric delay effects and avoids Geometry Base ( GB) errors, demonstrating significant advantages. The ambiguity resolution based on GIF model exhibits strong potential particularly in ionosphere-active environments and medium-to-long baseline scenarios.