jmc

We can simplify the congruence as follows (all of the following congruences are equivalent): $$\begin{array}{rl}34x+6& \equiv 2(\mathrm{mod}20)\\ 14x+6& \equiv 2(\mathrm{mod}20)\\ 14x& \equiv 16(\mathrm{mod}20)\\ 7x& \equiv 8(\mathrm{mod}10)\\ 21x& \equiv 8\cdot 3(\mathrm{mod}10)\\ x& \equiv 24(\mathrm{mod}10)\\ x& \equiv 4(\mathrm{mod}10)\\ x& \equiv \boxed{-6}(\mathrm{mod}10).\end{array}$$