A man starts walking from point A to point B at 4 km/hr. After 30 minutes, a woman starts from point A at 6 km/hr. If the woman reaches point B 20 minutes earlier than the man, then the distance…

The distance is $10$ kilometres. The man walks for $30+20=50$ minutes longer than the woman because he starts first and finishes last. For a distance $d$, that difference is $\frac d4-\frac d6=\frac d{12}=\frac56$ hours, giving $d=10$. Using just the thirty-minute head start gives $6$ kilometres.