To subtract the expressions, distribute each term in both parentheses:
12(z+4) = 12z + 12(4) = 12z + 48
3(14z+1) = 3(14z) + 3(1) = 42z + 3
Now, subtract the two expressions:
12z + 48 - (42z + 3) = 12z + 48 - 42z - 3 = -30z +45
Therefore, the final answer in fraction form is -30z + 45.