I'm going to assume the 4 and 3 are exponents and the expression is [tex]\left(3a^4\right)\left(-6a^3\right)[/tex].
The first step is to separate the coefficients of 3 and -6 from the variables and to multiply those as normal:
[tex]3 \cdot (-6) = -18[/tex]
As for the variables, you want to recognize that [tex]a^4[/tex] means [tex]a \cdot a \cdot a \cdot a[/tex] and [tex]a^3[/tex] means [tex]a \cdot a \cdot a[/tex], so
[tex]a^4 \cdot a^3 = \left( a \cdot a \cdot a \cdot a\right) \cdot \left(a \cdot a \cdot a\right)[/tex]
In total, there are 7 a's being multiplied, so
[tex]a^4 \cdot a^3 = a^{4+3} = a^7[/tex]
Putting this all together, we have:
[tex]\left(3a^4\right)\left(-6a^3\right) = 18a^7[/tex]
