Detecting hate speech in code-mixed language is vital for a secure online space, curbing harmful content, promoting inclusive communication, and safeguarding users from discrimination. Despite the linguistic complexities of code-mixed languages, this study explores diverse pre-processing methods. It finds that the Transliteration method excels in handling linguistic variations. The research comprehensively investigates machine learning and deep learning approaches, namely Logistic Regression and Bi-directional Gated Recurrent Unit (Bi-GRU) models. These models achieved F1 scores of 0.68 and 0.70, respectively, contributing to ongoing efforts to combat hate speech in code-mixed languages and offering valuable insights for future research in this critical domain.