We present the task description of the Detection and Classification of Acoustic Scenes and Events (DCASE) 2024 Challenge Task 2: First-shot unsupervised anomalous sound detection (ASD) for machine condition monitoring. Continuing from last year's DCASE 2023 Challenge Task 2, we organize the task as a first-shot problem under domain generalization required settings. The main goal of the first-shot problem is to enable rapid deployment of ASD systems for new kinds of machines without the need for machine-specific hyperparameter tunings. This problem setting was realized by (1) giving only one section for each machine type and (2) having completely different machine types for the development and evaluation datasets. For the DCASE 2024 Challenge Task 2, data of completely new machine types were newly collected and provided as the evaluation dataset. In addition, attribute information such as the machine operation conditions were concealed for several machine types to mimic situations where such information are unavailable. We will add challenge results and analysis of the submissions after the challenge submission deadline.