The letter you have posted contains your full name and address and the FPN number and I recommend you remove it and re-post with those details covered up.
I'm not an expert on this but paying some bloke on Facebook £50 to get rid your household rubbish was a criminal offence unless he had a Waste Carriers Licence and provided you with details of his Licence. Section 34 (2A) Environmental Protection Act 1990. I am guessing that he didn't show a Waste Carriers Licence because he didn't have one. Then - surprise, surprise - he just drove to somewhere he couldn't be seen and dumped it on a pavement, ie Flytipping. (Why didn't you just put it for collection by the council of the Borough you live in if it was just household waste?).
The problem for you is that if you use an unlicensed waste carrier and they dump it somewhere illegally then the people that generated the rubbish - you and the people who lve in your household - may be legally liable for the flytipping. Flytipping is an offence under the Environmental Protection Act 1990 and Dartford Council's Environmental Enforcement Policy says that the penalty notice they issue for flytipping is £500, which is what they have done.
What did you say in your appeal against the Fixed Penalty Notice? Dartford Council appear to be saying that as there was evidence of waste originating from four people at the address each of you are guilty of flytipping so they have issued each of you with a Penalty Notice. I would point you to section 5 (a) on page 18 of Dartford's Environmental Enforcement Policy which says:
"
Where waste comes from multiple individuals in the household, the ‘duty of care’ applies to the individual occupier of the property, who is arranging the transfer of household waste produced in/from that property. "
https://www.dartford.gov.uk/downloads/file/2243/environmental-enforcement-policy-november-2023That suggests to me that only the person who arranged for the bloke on Facebook to take the household's rubbish away (your brother) should have been given a penalty notice, not all four of you. Unfortunately for you normally councils only give you one opportunity to make 'representations'/appeals and as you have already done this you are now probably beyond the point where the council will consider any further apppeals or representations from you. Did the appeal say it was being made on behalf of all four of you?
So your options are for each of you to pay the £500 FPN you have received or any of you who fail to pay will be prosecuted in the Magistrates Court.
Whether you would have a defence if prosecuted I cannot say. Others may be able to advise. It would be helpful if you could post here your appeal to Dartford council and their response (cover up your name and address, penalty notice number, and any identifying details) so that we can see what admissions you made in your appeal.