ramesh lit the candle for two hours.
description:
thicker can lit for 6 hrs
thinner can lit for 4 hrs
if both lit for two hours then 6-2 =4 and 4-2= 2 will be 
left that will be twice of the length

Both are Equal length: L
Thick's burning rate: L/6
Thin's burning rate: L/4
After X hours (at bed time) of burning, remaining lengths:
Thick: L-(LX/6) and Thin: L-(LX/4)
But, at X hours, thick is twice as long as thin. i.e.:
L-(LX/6)=2[L-(LX/4)]
1-(X/6)=2-(X/2)
Solve for X and get 3.

the thicker candle lights for 6 hrs , so in 1 hr it will 
reduce in length by L/6

similarly the thinner candle will reduce in length by L/4.

 applying trial and check
 
 eg. after 3 hrs
 reduced length of thicker candle = L/6 *3 = 0.5 L
 there fore length remaining of thicker candle = L- 0.5 L
                                               = 0.25 L
similarly reduced length of thinner candle after 3 hrs
 =  L/4 * 3 = 0.75 L
 there fore length remaining of thinner candle = L-0.75 L
                                               = 0.25 L

 as can be seen length remaining of thicker candle is twice 
the length remaining of thinner candle.

Hay the eassiest way to understand the answer is :
just assume that the length of the candel is 12 cm
now the burning rate is as follow's
now the thinner will last upto 4 hours so the rate of 
burning will be 3cm/hr and for the thicker it will be 2cm/hr
Hours          Thinner             Thicker
First hour       3cm                 2cm
second hr        6cm                 4cm
third hr         9cm                 6cm

so after three hr's the length of the remaining candel is 
for THINNER it is 3 cm
for THICKER it is 6 cm
now the thicker is twice the length of thinner

Candles were ligthen till they last. CoZ there is no 
description that the candles were unlight them. How can u 
say that ramesh lit the candles for 2 or 4 hours.