"For me, nothing is impossible."
Translation:Bagi saya, tidak ada yang tidak mungkin.
They have the same meaning, but (if I'm not mistaken) I believe /bagi/ is more commonly used with personal names or pronouns. Or at least, that's the way I originally heard it, and I could be wrong.
According to the KBBI (an online Indonesian dictionary, https://kbbi.web.id/bagi), it seems like /bagi/ can do everything /untuk/ can do, but bagi is also used in expressing fractions in algebra, so maybe one can always swap in /bagi/ for /untuk/?