A particle moves along the $x-$axis over the time interval $0t6.$ The graph of the velocity of the particle is shown above. Over the time interval $0t6,$ the particle's displacement is $4$ and the particle traveled a total distance of $16.$

The area of A and $C$ are equivalent in the graph above.

What is the value of ${\displaystyle \underset{2}{\overset{4}{}}}v(t)dt$

a$.-12$

b$.-6$

c$.-4$

d$.0$

e$.8$