Let \begin{align} m_1 = 12\,\mathrm{kg}, \qquad m_2 = 4\,\mathrm{kg}, \qquad m_3 = 8\,\mathrm{kg} \end{align} If you solve this problem symbolically, then you'll find that the tension $T$ applied to mass $m_1$ satisfies \begin{align} T = \left(\frac{8m_1m_2m_3}{m_1m_2+m_1m_3+4m_2m_3}\right)g. \end{align} If you plug in the values given for the various masses, then you obtain \begin{align} T=\frac{192}{17}g \approx (11.30\,\mathrm{kg})g <\text{weight of mass $m_1$}, \end{align} so it seems that your claim
the tension would be greater than the greatest force of gravity of any mass
is false.