In this problem, we are asked to determine the degree of the given expression 12X4 - 8X + 4X2 -3. To answer this, first, we need to arrange the mathematical expression in descending order with respect to its power such as the new arrangement will become 12x4 + 4x2 -8x -3. The degree is clearly visible and it is 4. Therefore, the answer to this problem is the letter "B" which is 4.