The method of balancing redox equations is described here,
1: Separate into two half-reactions.
"CH"_3"CH"_2"CH"_2"CH"_2"OH" → "CH"_3"CH"_2"CH"_2"COOH"
"Cr"_2"O"_7^"2-" → "Cr"^"3+"
2: Balance all atoms other than H and O.
"CH"_3"CH"_2"CH"_2"CH"_2"OH" → "CH"_3"CH"_2"CH"_2"COOH"
"Cr"_2"O"_7^"2-" → color(red)(2)"Cr"^"3+"
3: Balance "O"
"CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH"
"Cr"_2"O"_7^"2-" → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"
4: Balance H.
"CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH" + color(brown)(4)"H"^+
"Cr"_2"O"_7^"2-" + color(brown)(14)"H"^+ → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"
5: Balance charge.
"CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH" + color(brown)(4)"H"^+ + color(magenta)(4)e^"-"
"Cr"_2"O"_7^"2-" + color(brown)(14)"H"^+ + color(magenta)(6)e^"-" → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"
6: Equalize electrons transferred.
3 × ["CH"_3"CH"_2"CH"_2"CH"_2"OH" + "H"_2"O" → "CH"_3"CH"_2"CH"_2"COOH" + color(brown)(4)"H"^+ + color(magenta)(4)e^"-"]
2 × ["Cr"_2"O"_7^"2-" + color(brown)(14)"H"^+ + color(magenta)(6)e^"-" → color(red)(2)"Cr"^"3+"+ color(blue)(7)"H"_2"O"]
7: Add the two half-reactions.
3"CH"_3"CH"_2"CH"_2"CH"_2"OH" + 2"Cr"_2"O"_7^"2-" + color(brown)(16)"H"^+ → 3"CH"_3"CH"_2"CH"_2"COOH" + color(red)(4)"Cr"^"3+"+ color(blue)(11)"H"_2"O"
8: Check mass balance.
"Atom"color(white)(m)"On the left"color(white)(m)"On the right"
color(white)(m)"C"color(white)(mmmm)12color(white)(mmmmml)12
color(white)(m)"H"color(white)(mmmm)46color(white)(mmmmml)46
color(white)(m)"O"color(white)(mmmm)17color(white)(mmmmml)17
color(white)(m)"Cr"color(white)(mmmml)4color(white)(mmmmmll)4
9: Check charge balance.
color(white)(mm)"On the left"color(white)(mm)"On the right"
color(white)(m)"4- + 16+ = 12+"color(white)(mml)"12+"
The balanced equation is
3"CH"_3"CH"_2"CH"_2"CH"_2"OH" + 2underbrace(color(orange)("Cr"_2"O"_7^"2-"))_color(orange)("orange") + 16"H"^+ → 3"CH"_3"CH"_2"CH"_2"COOH" + 4underbrace(color(green)("Cr"^"3+"))_color(green)("green") + 11"H"_2"O"
The color(orange)("orange dichromate ion" is converted to the color(green)("green chromium(III) ion").