Consider the following production function $Q=min \left(\frac{L}{2a}, \frac{K}{4b}\right)$. Let $w$ and $r$ be the wage and rental rate respectively The cost function associated with this production function is
$A) 2awQ\\
B) 4brQ\\
C) (wa + 2br)Q\\
D) None\; of\; the\; above$

What I have tried is:
We have the cost function $wL+rK=C$.
Since, here, the goods are perfect compliments, therefore, $\frac{L}{2a}=\frac{K}{4b}$.
Putting the value of $L$ in cost function we would get $\left(\frac{K}{2b}(wa+2br)\right)=C$.
Which would be C option if $Q$ can taken as $\frac{K}{2b}$. 
But I'm not sure about that.
 Please confirm?
The steps to optimally go from the Production function to the Cost function is to solve the cost-minimization problem for the firm, which determines the input mix given prices and some level of output, and in turn allows us to express one input with respect to the other (in this simplest two-inputs case).

When the production function is of the Leontief variety, optimal input mix is indeed determined by the equality stated by the OP, since by simple reasoning, any amount of one input above the amount satisfying the equality will incur the cost to  buy it but not any extra output.

Inserting the equality 

$$\frac{L^*}{2a}=\frac{K^*}{4b} \implies L^* = \frac {a}{2b}K^*$$ 

into the cost function we get Cost expressed as a function of one of the inputs only, $C^* = g(K^*)$ 

In order to eliminate it too, we turn again to the production function which can also be expressed as a function of one input at the optimal solution, 

$$Q = h(K^*) \implies K^* = h^{-1}(Q)$$

Inserting $h^{-1}(Q)$ into the Cost function we obtain

$$C = g\left[h^{-1}(Q)\right]$$

where also the various exogenous constants and prices will be present. In fact, this is easier done when the production function is Leontief, than when it is Cobb-Douglas for example, and so it should be easy for the OP to arrive at the correct solution.