Step-by-step Solution:

\[ \textbf{Step 1: Trace the path.} \] $$ \text{ Start at origin \(O(0,0)\). } $$ $$ \text{ Walk 8 km north \(\;\Rightarrow (0,8)\). } $$ $$ \text{ Turn right (east), walk 4 km \(\;\Rightarrow (4,8)\). } $$ $$ \text{ Turn right (south), walk 6 km \(\;\Rightarrow (4,2)\). } $$ $$ \text{ Turn left (east), walk 3 km \(\;\Rightarrow (7,2)\). } $4 \[ \textbf{Step 2: Distance from starting point.} \] Start point \(O(0,0)\), final point \(P(7,2)\). \[ OP = \sqrt{(7-0)^2 + (2-0)^2} = \sqrt{7^2 + 2^2} = \sqrt{49+4} = \sqrt{53}. \] \[ \boxed{\sqrt{53}\ \text{km (approximately 7.28 km)}} \]