Find the point on the curve
You have the curve expressed in vector form
Calculate (x'(t)) 2, (y'(t)) 2 and (z'(t)) 2 and simplify the square root of their sum. The result is a very simple expression.
Since the integrand (the square root) is a positive expression, the arclength increases as t increases. The given point, (0,-12,0) results when t=0 and hence to get a decreasing arclength you can integrate from t1 = 0 to a negative value of t2. Thus evaluate the integral and solve