[tex]\begin{array}{rl}\huge\text{Distance} & \huge\boxed{10\text{ km}}\\\\\huge\text{Displacement} & \huge\boxed{2\sqrt{13}\text{ km}}\end{array}[/tex]
Take a look at the diagram attached to this answer. Distance covered refers to the total distance the car moved from its starting point (the sum of the green lines) while displacement refers to how far the car ended up from its starting point (the dashed red line).
Distance covered
To find the distance covered, we can just add the movements together.
[tex]6+4=\boxed{10\text{ km}}[/tex]
Total displacement
Moving east and then north creates a right triangle, as one of the angles is [tex]90^{\circ}[/tex]. This means to find the displacement, we need to find the length of the hypotenuse (the longest side).
We can do this using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
Substitute in the two values we already know:
[tex]6^2+4^2=c^2[/tex]
Solve the powers and add:
[tex]\begin{aligned}36+16&=c^2\\52&=c^2\end{aligned}[/tex]
Take the square root of both sides and simplify:
[tex]\begin{aligned}\sqrt{52}&=\sqrt{c^2}\\2\sqrt{13}&=c\\c&=\boxed{2\sqrt{13}\text{ km}}\\c&\approx 7.211\end{aligned}[/tex]
