aw is correct, though I feel like answering your question anyway. Your function, indented nicely:
(define (List-coins Val Coin)
(cond ((= 0 Val) 1)
((< Val 0))
(else (+ (List-coins (- Val (car Coin)) Coin)
(if (null? Coin)
0
(List-coins Val (cdr Coin)))))))
This function will recurse until either Val is 0 or negative, or Coin is '()/null/the empty list. However, if Coin is the empty list, then your function will evaluate to
(+ (List-coins (- Val (car Coin)) Coin)
(if ...))
which contains a call to (car Coin), which throws the error that you observe. Instead, you should put the (null? Coin) check earlier, probably in the cond expression:
(define (List-coins Val Coin)
(cond ((= 0 Val) 1)
((< Val 0))
((null? Coin) 0)
(else (+ (List-coins (- Val (car Coin)) Coin)
(List-coins Val (cdr Coin))))))
This still won't work, because there's no else-clause in the ((< Val 0)) part of cond. In that case, Val is negative, and there's no way to meaningfully make change by adding more coins, so it should return 0. Adding this in:
(define (List-coins Val Coin)
(cond ((= 0 Val) 1)
((< Val 0) 0)
((null? Coin) 0)
(else (+ (List-coins (- Val (car Coin)) Coin)
(List-coins Val (cdr Coin))))))
