Let T be the total number of trays.
Let C be the total number of carton boxes.

(1) C = T + 26

(C x 12) – 6 = T x 30
=> 12C – 6 = 30T
=> 12C = 30T + 6
=> (2) C = (30T + 6)/12

Substituting (1) into (2), we get
T + 26 = (30T + 6)/12
12T + 312 = 30T + 6
18T = 306
T = 17

So he bought 17 x 30 = 510 eggs from the store #

sorry but I still don’t understand. Is there a simpler method?

Um… can someone else come up with a model answer?  I’m pretty bad at model answers.

The first equation C=T+26 simply states that there are 26 more carton boxes than trays.

The second equation  (C x 12) – 6 = T x 30 is now counting the actual number of eggs in each carton and tray.  So (Cx12) – 6 is the total number of eggs repackaged, which is of course equal the Tx30 which is the original number of eggs Mr Lee bought.

So I reworked the equation until I get C which I then substituted in the equation for C in the first equation.