Garbage Can
Garbage Bin, Trash Can, Trash Bin, Waste Can, Waste Bin, Rubbish Bin, Bin
noun
ゴミ means "garbage." Add a box to it and you have a garbage box aka a garbage can or garbage bin.
The reading is just the kun'yomi reading, the one you learned with the kanji. Be sure to pay attention to the rendaku though. はこ changes to ばこ.
ゴミ箱に、新せんな箱づめの魚がすてられていました。
There were boxed fresh fish in the garbage can.
そのゴミ箱の中にけっこん指輪があるかもしれないというかすかな希望がありました。
I had weakly hoped to find the wedding ring in the trash can.
ゴミ箱のゴミを捨てる時のあなたってとってもセクシーだと思うのよね。だから、ちょっと私のためにゴミ箱のゴミを捨ててくれないかな?
I think you are so sexy when you empty the garbage can— could you empty the garbage can for me please?