Your C implementation has a signed eight-bit char, likely uses ASCII, and, when converting an out-of-range value to a signed integer type, wraps modulo 2w, where w is the width of (number of bits in) the type. These are all implementation-defined; they may differ in other C implementations, with certain constraints.
char a = 'D', b='C', c='A'; initializes a to 68, b to 67, and c to 65.
a = c + 'D'; assigns 65 + 68 = 133 to a. Since 133 does not fit in char, it wraps to 133 − 256 = −123.
b = a + b + 'A'; assigns −123 + 67 + 65 = 9 to b.
c = b - a; assigns 9 − −123 = 132 to c. This wraps to 132 − 256 = −124.
a = a - b + 'C'; assigns −123 − 9 + 67 = −65 to a.
b = b - 68; assigns 9 − 68 = −59 to b.
printf("a=%c,b=%c,c=%d", a, b, c); prints a=?,b=?,c=-124 because a and b are codes for abnormal characters and the value of c is −124.