It is just as easy to solve it for any multiple of $48$ with undetermined $100\,$'s digit $\rm\:\color{#C00}j.$
Lemma $\rm\ 48\:|\:10^4 i + 100 \color{#C00}{\ j} + k\iff 4\:|\:k\ $ and $\rm\: j \equiv -4i-k/4\pmod{12}$
Proof $\rm\ mod\ 16\!:\ 10^4i+100\ j+k\equiv 4j+k,\:$ so $\rm\:16\:|\:4j+k\iff\ 4\:|\:k,\:\ j\equiv -k/4\pmod 4$
Further, $\rm mod\ 3\!:\ 10^4i+100\ j+k\equiv i+j+k,\:$ so $\rm\:3\:|\:i+j+k\iff j\equiv -i-k\pmod{3}$
By CRT these two congruences for $\rm\:j\:$ are equivalent to $\rm\:j \equiv -4i-k/4\pmod{12}\ \ $ QED
In your case $\rm\:62894\color{#C00}{\,j\,}52 = 6289\cdot 10^4 + 100\ \color{#C00}j + 4052\:$ we have $\rm\:i = 6289,\ k = 4052,\:$ therefore applying the Lemma we deduce that, $\rm\:mod\ 12\!:\ j \equiv -4(6289)-4052/4\equiv -5 -4\equiv 3.$ Finally, being a decimal digit, $\rm\:0\le j\le 9\:$ hence $\rm\:j \equiv 3 + 12\,n\:\Rightarrow\:j = 3.$