When renting out as a company via Hygglo, you need to bookkeep both your income and the cost to Hygglo.
The income you have in the company is the total amount of the rental price, what the customer paid for the rent (rent price minus booking fee). This is income with VAT. Then you have a cost to Hygglo for our commission (16% + VAT) which you bookkeep as a cost with ingoing VAT.
Bengt rents an ozone generator from Rentout AB for 200 kr. Then Rentout AB must bookkeep 160 kr income + 40 kr outgoing VAT. And 32 kr as a cost for Hygglo's commission and 8 k as ingoing VAT.