x + 2z = 0 .... (1)
2x - 3y = 4 .... (2)
Let x = t. Then y = (2t - 4)/3 and z = -t/2. This is the parametric equation of a line.
Your solution is not consistent with mine eg. My line does not pass through (0, 0, -4/3) but yours does (in fact, that point does not even lie in the second plane ....)