In this work, we propose a novel cross-talk rejection framework for a multi-channel multi-talker setup for a live multiparty interactive show. Our far-field audio setup is required to be hands-free during live interaction and comprises four adjacent talkers with directional microphones in the same space. Such setups often introduce heavy cross-talk between channels, resulting in reduced automatic speech recognition (ASR) and natural language understanding (NLU) performance. To address this problem, we propose voice activity detection (VAD) model for all talkers using multichannel information, which is then used to filter audio for downstream tasks. We adopt a synthetic training data generation approach through playback and re-recording for such scenarios, simulating challenging speech overlap conditions. We train our models on this synthetic data and demonstrate that our approach outperforms single-channel VAD models and energy-based multi-channel VAD algorithm in various acoustic environments. In addition to VAD results, we also present multiparty ASR evaluation results to highlight the impact of using our VAD model for filtering audio in downstream tasks by significantly reducing the insertion error.