Mumsnet is not generally a great resource for things like this. First you have 36 months from the date he entered the care home to sell without losing private residence relief from capital gains tax.
If the home is sold after the father dies after capital gain is taxed on the gain between value at death and the final price. The house may not increase in value by a lot if sold quickly and each of the 6 can set their capital gains allowance against the tax. It's only 3k each but better than nothing.
If sold now a trust could be set up to either pay care home fees or pass the proceeds to the children. I know too little about trusts to comment further.
One of the children could move into the house if a proper legal agreement is drawn up for a later sale or buying the others out.
Moving into a care home does not remove the right to relief from inheritance tax if the value of the family home is based to descendants
"The additional nil-rate band will also be available when a person downsizes or ceases to own a home on or after 8 July 2015 and assets of an equivalent value, up to the value of the additional nil-rate band, are passed on death to direct descendants.
There will be a tapered withdrawal of the additional nil-rate band for estates with a net value of more than £2 million. This will be at a withdrawal rate of £1 for every £2 over this threshold.
The existing nil-rate band will remain at £325,000 from 2018 to 2019 until the end of 2020 to 2021."
There may be 2 nil rate bands if the house was jointly owned and the wife died first.
In summary there is no immediate need to sell the property and depending on the amount of other assets inheritance tax may not be payable at 40%,