A short-day plant ($\text{SDP}$) has a critical day length of $14$ hours. It will successfully initiate flowering when the ambient day length is:

Short-day plants require a continuous period of darkness exceeding a critical threshold, meaning they flower only when the photoperiod (day length) is strictly less than their critical day length. Since $12$ hours is less than the critical threshold of $14$ hours, the plant will flower under this condition.