What I understand:
This question asks to solve for $t$ such that when $(3619 \times t)$ is divided by $4557$ the remainder is $133$
I have found a Bezout identity
$7 = 34 \times 3619 - 27 \times 4557$ and
$1 = 34 \times 517 - 27 \times 651$ and
and I see that $133 = 7 \times 19$ so
$133 = 646 \times 3619 - 513 \times 4557$
Somehow we are supposed to arrive at $t \equiv 646 \pmod{651}$ and I feel like I've worked out all the bits and pieces but having trouble putting it together