Wow, that's backward from how I would do it.
I suggest starting with the BAB and adding the other bonuses, then applying the penalties. Makes no sense to start with the penalties (or, at least, the math is harder if you do). Also, there is no reason to even include the regular penalties for fighting with two weapons in this math since you have the TWF feat, so it's basically just one extra attack but with a -4 penalty on all attacks.
You were nearly right, but the Improved Two Weapon Fighting feat gives you a second off-hand attack, but it's not at specifically -5, it's at whatever your first off-hand attack should be but then you subtract 5 from that.
I am also assuming you're using two battleaxes, one-hand martial melee weapons. Not greataxes (which you cannot use two at the same time) and not handaxes (which would have smaller penalties since they are light weapons).
So let's reverse it (I put the off-hand attacks in parentheses for clearer understanding):
BAB: +6/+1
STR and Weapon Focus: +10/+5
Off-hand before penalties: +10/(+10)/+5
Off-hand with penalties, adjusted for TWF feat: +6/(+6)/+1
Improved TWF feat: +6/(+6)/+1/(+1) (the 2nd off-hand attack is -5 below the first off-hand attack)
Your damage is correct.
None of this considers magical weapons or other bonuses (such as magic spells or Favored Enemy bonuses), of course.
Finally, if I was wrong and you were using handaxes, then all those numbers should be higher because the TWF penalties with light weapons would only be -2, not -4, so the adjusted values would be: +8/(+8)/+3/(+3)
And to add what DM_Blake said, only your offhand weapon has to be a light weapon to get the -2 (instead of a -4).
And to add to that, if you use the same weapon in both hands, your Weapon Focus feat will apply to both weapons. I assumed this in my previous post. But if you use two different weapons, say, a battleaxe and a handaxe, you would need two Weapon Focus feats (one for each weapon) or, if you don't have both Weapon Focus feats, make sure to only apply the +1 to hit to the correct weapon that matches your feat selection.
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And to add what DM_Blake said, only your offhand weapon has to be a light weapon to get the -2 (instead of a -4).And to add to that, if you use the same weapon in both hands, your Weapon Focus feat will apply to both weapons. I assumed this in my previous post. But if you use two different weapons, say, a battleaxe and a handaxe, you would need two Weapon Focus feats (one for each weapon) or, if you don't have both Weapon Focus feats, make sure to only apply the +1 to hit to the correct weapon that matches your feat selection.
And if you have any other number of bonuses or penalties that apply to both/single weapons independently then they either apply or don't apply as appropriate--none of which are anywhere near important enough to merit a mention as my addendum to your post.