The problem is that the same parameter is being used in both equations. They should have ben written:

L1 : x=12+3t, y=5+3t, z=5+t

L2 : x=-5+4s, y=-14+5s z=-6+4s

Now equate:

12 + 3t = 5 + 4s .... (1)

5 + 3t = -14 + 5s .... (2)

5 + t = -6 + 4s .... (3)

Solve two of these equations simultaneously and check that the solution satisfies the third.