226

a)
$92=15\cdot6+2$
$92\equiv2\ \left(mod\ 6\right)$
$903=150\cdot6+3$
$903\equiv3\left(mod\ 6\right)$
$92\cdot903\equiv2\cdot3\equiv0\left(mod\ 6\right)$
b)
$13=2\cdot6+1$
$5=0\cdot6+5$
$13^{19}+5\equiv1^{19}+5=1+5=0\left(mod\ 6\right)$
c)
$7=1\cdot6+1$
$-1=0\cdot6-1$
$7^{12}-1\equiv1^{12}-1=1-1=0\left(mod\ 6\right)$