Dehydration and Electrolyte Imbalance: Given the patient hasn't eaten in 24 hours and is undergoing chemotherapy, dehydration and electrolyte imbalances are common and can cause dizziness and double vision due to their effects on the nervous system and muscle function.

Chemotherapy-induced Neurotoxicity: Certain chemotherapeutic agents can cause neurotoxic effects, including neuropathy and cerebellar dysfunction, leading to symptoms like dizziness and double vision.
Hypoglycemia: Not having eaten for 24 hours increases the risk of hypoglycemia, which can cause dizziness, confusion, and visual disturbances including double vision.
Medication Side Effects: Many medications used in the management of chemotherapy side effects or for other conditions can cause dizziness and double vision as side effects.

Cerebral Metastases or Leptomeningeal Disease: In a patient with cancer, new neurological symptoms like double vision and dizziness could indicate cerebral metastases or leptomeningeal disease, which are serious and require immediate attention.
Stroke or Transient Ischemic Attack (TIA): Although less likely, stroke or TIA must be considered, especially if there are other focal neurological deficits, as these conditions are medical emergencies.
Infection (e.g., Meningitis, Encephalitis): In immunocompromised patients, such as those undergoing chemotherapy, infections can present with non-specific symptoms including dizziness and visual disturbances.

Wernicke's Encephalopathy: A rare but serious condition caused by thiamine deficiency, which can occur in malnourished patients, including those with prolonged periods without eating. It presents with confusion, ataxia, and ophthalmoplegia.
Paraneoplastic Syndromes: These are rare disorders that are triggered by an altered immune system response to a neoplasm, and can cause a variety of neurological symptoms, including double vision and dizziness.