Mogu li platiti karticom? means “Can I pay by card?” – more useful than the statement when you do not know whether cards are accepted.
The waitress asks whether the card will still be good tomorrow, otherwise it will be a burden on her pocket: tomorrow and pocket give you mogu li. You put the card on a plate with two animals pictured on it – plate and two animals give you platiti. And the card is once again the one with the tiger from the zoo: karticom.
Note that platiti and plaćam have two different images: the plate with the animals versus the splashing with the ants.