Here, you're trying to find the derivative of a function defined as the dot product of two vectors. First, we need to take stock of what we know: the explicit value of u(2) and u'(2), as well as the equation form of both f(t) and v(t). What we need to do is find a way to take that given information and covert it into something that will give us the value of f'(2).
The first thing to note is that the derivative of a dot product follows the standard product rule1, so d(a•b)/dt = (da/dt)•b + (db/dt)•a. This will let you find the explicit form for f'(t). Next, you're going to want to use the rules for finding the derivative of a vector valued function to find v'(t); fortunately, this can be done just by taking the derivative of each term of the vector. Then you're going to need to plug in t=2 to find the resulting vectors for v(2) and v'(2). Since these values are given for u(2) and u'(2), all that is left is to do the resulting dot products, add the results, and you will have the solution for f(t).
Hope this helps!
1If you're confused about why the product rule would necessarily hold for dot products as well, there's a neat proof here: https://proofwiki.org/wiki/Derivative_of_Dot_Product_of_Vector-Valued_Functions
