Modulo Arithmetic equations

Question

How to find the value of the unknown in the equations . I have tried finding the value y by equating the left hand side to the right hand side $\;20\pmod 9 = y\pmod6$, find the value of $y$

Answer 1

Hint:

First of all, reduce the equation: as $20\equiv 2\mod 9$, the equation is $$ˆy\mod 6= 2\mod 9$$ Next, translate what it means in a concrete way: there exist $k,\ell\in \mathbf Z$ such that $$y+6k=2+9\ell\iff y=2+9\ell-6k.$$ Last: think of Bézout's identity.