Let i,j,k represent unit vectors in x,y,z axis.
Initially the body was at origin so it's position vector was R1= 0i+0j+0k.
After the motion the position vector is R2=8i+6j+10k.
Therefore displacement vector( change in position vector) becomes R=R2-R1
Magnitude of displacement vector is given by √(8^2+6^2+10^2)=10√2 m.