Final answer:
The described X-ray findings, biopsy results, and 11;22 translocation suggest a diagnosis of Ewing's sarcoma, which is a malignancy commonly found in the bones of children and adolescents.
Step-by-step explanation:
The question refers to a case where X-ray imaging indicates an onion skin like periosteal reaction, and a bone biopsy (Bx) reveals small, round, blue cells. Given the described 11;22 translocation, these findings are consistent with a diagnosis of Ewing's sarcoma, which is a type of bone cancer commonly affecting children and adolescents. Ewing's sarcoma is recognized for these particular clinical and pathological features. The 11;22 translocation results in a fusion gene that is characteristic of this disease.