Final answer:
The investigation of choice to confirm the diagnosis is an abdominal X-Ray Erect film.
Step-by-step explanation:
The investigation of choice to confirm the diagnosis in this case would be Abdominal X-Ray Erect film.
Given the patient's presentation of severe abdominal pain, colicky in nature, with no bowel movement for 3 days, vomiting, dehydration, and a mass in the right inguinal area that disappears when lying on the back, it is highly suspicious for obstructive bowel disease, specifically an inguinal hernia.
An abdominal X-ray in an erect position would be the most appropriate investigation to confirm this diagnosis. It can show visually the presence of bowel obstruction, air-fluid levels, and the presence of a hernia.