Hi, Casanova,
I started with A. This number has six letters, and there are only six possibilities, of which four can be quickly rejected because they finish with zero, and the answer to clue a can't start with a zero.
The alphabetic sum of the distinct letters (ASDL) is the answer to clue n. Calculate both ASDLs for the two possibilities for clue A, and you should find that only one of these has 10 letters when spelt out. Working out the ASDL for this number will give you the answer to clue G, and working out the ASDL for clue G will give you the answer to clue d, which in turn will give you the answer to clue F.
There's very little need for trial and error. It's useful to remember that three-digit numbers will include the string HUNDRED AND, which has 10 letters, so for example the answer to clue B, which has 16 letters, must begin with ONE, TWO or SIX and end with ONE, TWO or SIX (not TEN, which would make the answer to clue c begin with zero).