Question 687037
To factor by grouping, you want to find similar terms.  With {{{3a^3+2a^2+6a+4}}}, the easiest way to group is by looking at the numbers in front of the variables and seeing if any of the numbers are factors of each other.  3 and 6 are factors of 6, and 2 and 4 are factors of 4.  So, let's try grouping 3a^3 and 6a together, and 2a^2 and 4 together:

{{{(3a^3+6a)+(2a^2+4)}}}

In the first set of parenthesis, we can factor out 3a:

{{{3a(a^2+2)}}}

In the second set of parenthesis, we can factor out a 2:

{{{2(a^2+2)}}}

Putting these both together, results in:

{{{3a(a^2+2)+2(a^2+2)}}}

As you can see, there are two sets of {{{(a^2+2)}}}

We can group these together, and then, in another set of parenthesis, group the remaining terms together:

{{{(3a+2)(a^2+2)}}}, which is our final answer