Two decisions: which classification, then which grade.
Decision 1 - pick the right system. The X-ray is of the elbow showing a break in the distal humerus just above the condyles - a supracondylar humerus fracture. The eponymous system for this exact injury is Gartland. Salter-Harris is reserved for fractures that cross the growth plate (physis); since this is a metaphyseal supracondylar break, Salter-Harris does not apply - so options B and D are out immediately.
Decision 2 - grade the displacement. Gartland grades supracondylar fractures by how displaced they are:
• Type I = no displacement
• Type II = angulated but the posterior cortex still hinges
• Type III = completely off, no cortical contact
The film shows the distal fragment fully translated with no bony continuity → a complete displacement → type III.
Why not Gartland type 4? Type IV is a rare, intra-operatively diagnosed multidirectionally unstable pattern, not the typical fully-displaced film shown here.
Putting it together: right system = Gartland, right grade = III. Answer: Gartland type 3 (Option A).