The odds ratio summarises a case-control study by comparing the odds of being exposed in the diseased group with the odds of being exposed in the non-diseased group.
First build the odds of exposure in each arm. Among the 80 cases, 60 are exposed and 20 are not, so the exposure odds in cases are $60/20 = 3$. Among the 120 controls, 40 are exposed and 80 are not, so the exposure odds in controls are $40/80 = 0.5$.
The odds ratio is the ratio of these two odds:
\[ OR = \frac{60/20}{40/80} = \frac{3}{0.5} = 6 \]
This is algebraically identical to the diagonal cross-product $ad/bc$, which confirms the value. Because the result exceeds 1, the exposure is associated with markedly higher odds of disease — roughly a sixfold increase. Values such as 1.5 or 0.17 would come from dividing the odds the wrong way round or pairing the wrong cells.
\[\boxed{OR = 6}\]