To determine the relative order of rate constants in the given transformations, let's analyze the reactions shown in the image:

1. The transformations depicted are reactions involving stereochemistry where the arrangement of groups around the chiral center plays a crucial role. The rate of reaction is influenced by the relative stability of these stereoisomers and the steric effects.
2. For the \(k_1\) and \(k_2\) reactions, where PhSNa (sodium thiophenoxide) is used:
   • \(k_2\) involves the attack on the less hindered side of the substrate. It involves the equatorial position, which is more favored due to reduced steric hindrance.
   • \(k_1\) involves attack on the axial position, which is relatively more hindered.
   • Hence, \(k_2 > k_1\) is expected as per the observation that equatorial substitutions generally proceed faster due to less steric hindrance.
3. For the \(k_3\) and \(k_4\) reactions using \(CrO_3\):
   • \(k_4\) also prefers the equatorial position, which involves less steric hindrance compared to the axial one.
   • The equatorial attack leads to a more stable intermediate and hence a faster reaction rate.
   • Therefore, \(k_4 > k_3\) since it involves the more favorable equatorial position.

Considering these stereochemical factors and steric effects, the correct order of rate constants is \(K_2 > K_1\) and \(K_4 > K_3\).

Thus, the correct answer is: \(K_2 > K_1; K_4 >K_3\).