The correct answer is C. 2.
A (6, 4) block code means that the code has 6 bits, but only 4 of those bits are used to represent the original message. The other 2 bits are used for error correction. The minimum distance, dmin, is the number of bits that need to be flipped in order to change the codeword into a different codeword. In this case, dmin = 3, which means that if 3 or fewer bits are flipped, the decoder will be able to correct the error.
For example, let's say the original message is 10101. The codeword that is transmitted is 10110. If there is a single error and the 1 in the third position is flipped to a 0, the received codeword will be 10010. The decoder will be able to correct this error because the distance between the transmitted codeword and the received codeword is 2, which is less than or equal to dmin.
However, if there are two errors, such as if the 1 in the third position is flipped to a 0 and the 1 in the fifth position is flipped to a 0, the received codeword will be 10000. The decoder will not be able to correct this error because the distance between the transmitted codeword and the received codeword is 3, which is greater than dmin.
In conclusion, a (6, 4) block code can correct up to 2 errors.