The main purpose of this study is to evaluate the safety of the study drug known as Prexasertib (LY2606368) in participants with advanced cancer or cancer that has spread to other parts of the body. This study will involve a single dose of ¹⁴C radiolabelled Prexasertib . This means that a radioactive substance, carbon 14, will be incorporated into the study drug. This will provide information about the study drug and its breakdown products and will help determine how much passes from the blood into urine, feces and expired air. After a minimum 14-day washout period following the [¹⁴C] Prexasertib dose, participants will be allowed to receive continued access to Prexasertib as outpatients.

Inclusion Criteria:

• Have a histological or cytological diagnosis of cancer (solid tumour), with clinical or radiologic evidence of locally advanced and/or metastatic disease, for which no life-prolonging therapy exists
• Have the presence of measurable and/or nonmeasurable disease as defined by the Response Evaluation Criteria In Solid Tumours
• Have Body Surface Area (BSA) greater than or equal to (≥)1.62 meter squared (m²) and less than or equal to (≤) 1.90 m²
• Have adequate organ function
• Have a performance status of ≤2 on the Eastern Cooperative Oncology Group (ECOG) scale
• Have an estimated life expectancy, in the judgment of the investigator, that will permit the participant to complete 1 full cycle of treatment (beyond the initial [¹⁴C]prexasertib dose)

Exclusion Criteria:

• Have received treatment within 28 days of the initial dose of study drug with an investigational product or non-approved use of a drug or device
• Have serious pre-existing medical conditions (left to the discretion of the investigator)
• Have symptomatic central nervous system (CNS) malignancy or metastasis (screening not required)
• Have current haematologic malignancies or acute or chronic leukaemia
• Have an active fungal, bacterial, and/or known viral infection
• Have participated in a ¹⁴C (carbon) study within the last 6 months prior to screening for this study
• Have a second primary malignancy that in the judgment of the investigator and sponsor may affect the interpretation of results