Precalculus, Chapter 6, 6.3, Section 6.3, Problem 71

You need to find the component form of the vector v = , hence, you need to use the information provided.
You need to evaluate the magnitude |v|, such that:
|v| = sqrt(a^2+b^2)
2sqrt3 = sqrt(a^2+b^2)
The direction angle of the vector is theta = 45^o , hence, you may use the following formula:
tan theta = b/a => tan 45^o = b/a => 1 = b/a => b = a
Replacing a for b yields:
2sqrt3 = sqrt(a^2+a^2) => 2sqrt3 = +-a*sqrt2 => a = +-sqrt6 => b = +-sqrt6
Hence, evaluating the components of the vector v, yields or <-sqrt6,-sqrt6>.