Creating a custom year between two dates for a measure, e.g. 12 August 2019 to 12 August 2020

Bemused , Based on initial Description

Means from

12 August 2019 to 11 August 2020

Calendar = calendar(Date(2019,08,12),Date(2020,08,11))  // New calendar table 

Start of year = Startofyear([Date], "08/11")

Endof year = Endofyear([Date], "08/11")

Start of month = eomonth([Date], -1) +12

End of month = eomonth([Date], 0) +11 

Based on Start date month, year , you can create Rank and use that for Current Vs prior

Year Rank = RANKX(all('Date'),'Date'[Year Start date],,ASC,Dense)

Measure
This Year = CALCULATE(sum('Table'[Qty]), FILTER(ALL('Date'),h'Date'[Year Rank]=max('Date'[Year Rank])))
Last Year = CALCULATE(sum('Table'[Qty]), FILTER(ALL('Date'),'Date'[Year Rank]=max('Date'[Year Rank])-1))

Power BI — Year on Year with or Without Time Intelligence
https://medium.com/@amitchandak.1978/power-bi-ytd-questions-time-intelligence-1-5-e3174b39f38a
https://www.youtube.com/watch?v=km41KfM_0uA

Power BI — Month on Month with or Without Time Intelligence
https://medium.com/@amitchandak.1978/power-bi-mtd-questions-time-intelligence-3-5-64b0b4a4090e
https://www.youtube.com/watch?v=6LUBbvcxtKA