One of the most dangerous diseases in modern times is generally thought to be lung cancer. Colon cancer will be the second biggest killer of Americans in 2023 when it comes to cancer. The most precise diagnosis technique involves the utilisation of histopathology pictures obtained from biopsies. Histopathological image analysis is the process of carefully looking through tissue samples from people with lung and colon cancer to find cancerous cells and tumours. This research is very important for figuring out the stage of the tumour, which makes diagnosis easier, predicts the prognosis, and helps plan treatment. Lung and colon cancer are significant public health issues that require continuous efforts in prevention, early identification, and effective therapeutic options. This approach employs deep learning, namely the EfficientNet architecture. The study employs several image resolutions and applies transfer learning and parameter tweaking techniques to improve performance. Utilising the LC25000 dataset, the proposed approach attains a notable degree of precision, with EfficientNetB0 emerging as the most accurate model, achieving a flawless score. The study emphasizes the ability of deep learning to automate the classification of cancer-related histopathology images, hence improving the efficiency and accuracy of diagnostic operations. The study addresses the inherent black box nature of deep learning (DL) models by emphasizing the importance of explainability in understanding their predictions. To visualize and interpret the decision-making process of EfficientNetB0 predictions, the study employs lime, a method known for generating visual saliency maps. This allows to identify and highlight the most activated areas in input images, providing valuable insights into the features influencing the DL model′s class predictions.