Surprisingly difficult to find a good image to illustrate this. I think the description in Wikipedia is as clear as any I've read:
The Exchequer was named after a table used to perform calculations for taxes and goods in the medieval period. According to the Dialogue concerning the Exchequer, an early medieval work describing the practice of the Exchequer, the table was large, 10 feet by 5 feet with a raised edge or "lip" on all sides of about the height of four fingers to ensure that nothing fell off it, upon which counters were placed representing various values. The name Exchequer referred to the resemblance of the table to a chess board (French: échiquier) as it was covered by a black cloth bearing green stripes of about the breadth of a human hand, in a chequer-pattern. The spaces represented pounds, shillings and pence. Wikipedia
The Exchequer’s rather unusual name was derived from the chequered cloth on which the confrontational audit process took place between the powerful Barons of the upper Exchequer and the hapless accountants summoned before them, who were regularly interrogated about the state of their accounts. The cloth was used to visually record the sums of money that were demanded and received, and an accountant was only discharged of their debt on the provision of evidence – a writ authorising expenditure on behalf of the Crown, or a wooden tally denoting that a payment had been made into the lower Exchequer. history.blog.uk
"Before decimalisation, the pound was divided into 20 shillings and each shilling into 12 pence, making 240 pence to the pound." Pound Sterling
Even addition and subtraction can be challenging in a pre-decimal pound. If I have a debt of 31L, and I pay 7s2p every year, how long will it take to pay off the debt?
I don't have a clear source/citation, but I have always assumed that the checkered pattern served as a form of place value. When there are 13p in a square, remove them all and place 1s in the next square; if that square now hoas 2os, remove and place 1L in the next, etc.
The eminent Mr. Geerkens points out: (I'm repeating here only because comments are ephemeral, and the substance is, I think, important enough to be part of the answer.)
As this is occurring in roughly the two centuries before the widespread adoption of double-entry bookkeeping, it might be a sort of precursor to that - with Assets and Liabilities in two separate sets of columns. The Missing Dollar riddle is a perfect example of how easily one's intuition can be fooled without a rigorous accounting method in place.
Two quick points: 1) Accrual accounting and the Income Statement are 19th century developments. Everything is Cash accounting before that. 2) Modern Balance Sheet divides the RHS into Liabilities and Equities - but note Equities really means Claims. Originally the RHS distinction was between debt equities and ownership equities.
I have half a mind to experiment with the missing dollar problem on a virtual exchequer.