This is the 12908th most frequent Russian word.
ленточкой
"Ленточкой" means "with a little ribbon" or "as a small ribbon" in English.
The word 'ленточкой' is used in the instrumental case here to indicate the means by which the gift is tied.
Она перевязала подарок красной ленточкой.
She tied the gift with a red ribbon.
The word 'ленточкой' is in the instrumental case, denoting that the gymnast is performing the dance using the ribbon as an accessory.
Гимнастка красиво танцевала с ленточкой.
The gymnast beautifully danced with a ribbon.
Here, 'ленточкой' is instrumental case, describing the decoration medium or material utilized for the painting.