Artificial intelligence (AI) is considered an efficient response to several challenges facing 6G technology. However, AI still suffers from a huge trust issue due to its ambiguous way of making predictions. Therefore, there is a need for a method to evaluate the AI's trustworthiness in practice for future 6G applications. This paper presents a practical model to analyze the trustworthiness of AI in a dedicated 6G application. In particular, we present two customized Deep Neural Networks (DNNs) to solve the Automatic Modulation Recognition (AMR) problem in Terahertz communications-based 6G technology. Then, a specific trustworthiness model and its attributes, namely data robustness, parameter sensitivity, and security covering adversarial examples, are introduced. The evaluation results indicate that the proposed trustworthiness attributes are crucial to evaluate the trustworthiness of DNN for this 6G application.