To solve this problem, we need to identify the feature that distinguishes a male cockroach from a female cockroach. Let's analyze each option:$\newline \bullet$Option 1: Forewings with darker tegmina$\newline$ - Tegmina are the leathery forewings of cockroaches. Both male and female cockroaches have tegmina, and the color is not a reliable distinguishing feature between the sexes.$\newline \bullet$Option 2: Presence of caudal styles$\newline$ - Male cockroaches have a pair of short, unsegmented appendages called caudal styles located on the 9th abdominal segment.$\newline$ - Female cockroaches do not have caudal styles.$\newline$ - This is a distinguishing feature of male cockroaches.$\newline \bullet$Option 3: Presence of a boat-shaped sternum on the 9th abdominal segment$\newline$ - Both male and female cockroaches have a sternum on the 9th abdominal segment, but it is not a distinguishing feature between the sexes.$\newline \bullet$Option 4: Presence of anal cerci$\newline$ - Anal cerci are paired appendages found in both male and female cockroaches, so they cannot be used to distinguish between the sexes.$\newline$Based on the analysis, the correct feature that identifies a male cockroach is the presence of caudal styles.$\newline$Therefore, the correct option is Option 2.