First group the coefficients and variables.

– 3x²(4x³) = (– 3 · 4) (x² · x³)

=  (– 12) (x² · x³)            (Multiply:  – 3 · 4 = – 12)

Since base is common, apply the product of powers property: a^m · aⁿ = a^{m + n}.

=  (– 12) (x^{2 + 3})

=  – 12x⁵                        (Add exponents: 2 + 3 = 5)

Product of  – 3x²(4x³) is – 12x⁵.