"장바구니는 카트보다 무겁습니다."
Translation:The shopping basket is heavier than the cart.
장바구니는 : shopping basket (+topic particle)
카트 : cart
보다 : put after a noun for comparison, translating as "compared to" (or the way they did here, with "-er" after the adjective. You can remember it by thinking that when you compare something to something else, you look (보다) at it.
무겁습니다 : formal form of 무겁다, to be heavy
The shopping basket is heavy compared to the cart, becomes, the shopping basket is heavier than the cart.