This is the 12394th most frequent Russian word.
карточкой
"Карточкой" means "by card" or "with a card," typically referring to payment methods.
The word 'карточкой' is the instrumental case of 'карточка', meaning 'card', and its usage here shows the tool or means by which the purchase is paid.
Я оплачивал покупку карточкой.
I paid for the purchase with a card.
Here, 'карточкой' indicates the possession or context of the photo being on the card, demonstrating a format or medium.
Покажи мне свою фотографию на карточке.
Show me your photo on the card.
In this example, 'карточкой' refers to the means or instrument (a card) used to control something (the door).