In a certain base b, the statement $3\times 4=15$ is correct. The value of b is:

The product three times four is twelve whatever base we write it in. The symbol 15 in base b means b + 5, so b + 5 = 12 and b = 7. This is consistent, because the digit 5 needs a base larger than 5. Check in base seven: twelve = 1 seven + 5 units, written 15.