Step 1: The radiograph shows anterior subluxation of one lumbar vertebra over the one below it - the classic appearance of spondylolisthesis (here L5 slipping anterior to S1).
Step 2: Spondylolisthesis is forward slippage of a lumbar vertebra, most often at L3-L4, L4-L5 or L5-S1. It results from a defect in the pars interarticularis (spondylolysis).
Step 3: In older patients (over 60) it commonly occurs with osteoarthritis and minimal trauma, fitting this 65 year old lady with backache.
Step 4: Spondylolysis (option c) is only the pars defect without slippage, osteoporosis (a) causes diffuse demineralisation, and discitis (d) is disc-space infection - none match a visible vertebral slip, so spondylolisthesis is correct.