The dot product of two vectors is the sum of the product of each pair of corresponding vectors, and the result is a scalar value, not a vector
u = <4, -4, 4>
v = <4, 2, -4>
w = <0, -2, -1>
u·v = 4*4 + (-4)*2 + 4*(-4) = 16 - 8 - 16 = -8.
(u·v)u = -8u
Just multiply each component of u by -8.
Find the dot product of the last answer times the original u vector.
u·v = -8, from above
v·w you can find the same way, with vectors v and w instead of u and v
Once you find this, just add the two values together.
I hope this helps. If you have further questions, please comment.