Great point...it's definitely not intuitive to factor out the 3^(x-1) term, and that's why this is a tough question.
One way to approach a problem like this, one with kind of vague numbers, is to do a quick "parallel" problem using small numbers.
So, here, the left hand side of the equation is:
3^x - 3^(x-1) =
Well, that's awkward...it's hard-to-visualize exponents. But try with small numbers to see the relationship and you'll better understand the concept. If x were to be 4, then
3^4 - 3^3 =
Well, here, it's clearer that the second term is common with the first. You could factor out 3^3 from both terms to get:
3^3 (3^1 - 1)
3^3 * 2
Seeing this, it may be clearer that the 3^x term is really the 3^(x-1) term just multiplied by one more 3. So you can factor out the smaller number, 3^(x-1), because of that.
Or, you can rephrase 3^x in the original equation as: 3^(x-1) * 3^1
The reason you'd do that is because you want to find common terms to factor out, and by using the rule that x^y * x^z = x^(y+z), you can break apart x into x - 1 and 1 to get that common term.
Either way, that's how you can factor out the common 3^(x-1) term as done in the explanation above...