[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \bold{Given:}\begin{cases} f(8) = 10 \\ f(n) = nf(n - 1) + 2 \end{cases} \\ \\ \text{Consider } f(n) = nf(n - 1) + 2. \\ \\ \text{For }n=9, \text{we get} \\ \\ f(9) = 9f(8) + 2 = 9(10) + 2 = 92 \\ \\ \text{Now continue} \\ \\ f(10) = 10f(9) + 2 = 10(92) + 2 = 922 \\ \\ f(11) = 11f(10) + 2 = 11(922) + 2 = 10,\!144 \\ \\ f(12) = 12f(11) + 2 = 12(10,\!144) + 2 = 121,\!730 \\ \\ \therefore \boxed{f(12) = 121,\!730} \end{array} [/tex]
