This study examines the multiplicative problem-solving strategies used by a 14-year-old student with autism spectrum disorder and intellectual disabilities during an instructional process based on the Conceptual Model-based Problem Solving (COMPS) approach. The instruction aimed to enhance conceptual comprehension of problem-solving by the use of model diagrams representing mathematical relations involved in word problems. These diagrams aid in selecting the appropriate operation for each type of multiplicative problem, including equal-groups, multiplicative comparison, and combination problems. We further discuss how the instructional process promoted conceptual understanding for the three problem types, highlighting the development of strategies (modeling, counting, and operations) and the pivotal role of the COMPS methodology components in this progression. The results indicate that the student adeptly adopted the COMPS approach, facilitating the transition from informal modeling to written operations, with his choice of strategies varying depending on the type of problem. While there was a higher utilization of modeling strategies in equal-groups and combination problems, modeling was not as frequently employed in comparison problems. We speculate how this differentiated strategy preference could be associated with certain characteristics of the disorder.