Ok, I can have a go at helping you. The way tax credits is worked out is by allocating you a series of 'elements', and then deducting from those elements according to your income. If you run out of deductions, you get to keep what's left. That becomes your tax credit award. If your deductions exceed your 'elements', then your tax credit award is zero.
The first thing that sticks out for me, is that they are saying that they are still using an estimated income for 2015-2016. You should be able to give them an actual income by now - it's a whole year later, so you need to update them.
Your income for tax credits 2015-2016 is £38,278 (page 3). Your allowance before deductions is £6420, which means that £31,858 will be subject to a withdrawal rate of 41%. So, £13,061 will be deducted from any award that is calculated. But it is removed in a certain order.
Your working tax credits award is as follows:
Basic element: £1960.05
Couple element: £2011.15
30 hour element: £810.30
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Total: £4781.50
But, you have £13,061 to remove, so £4781.50 is deducted, making it £0.
That reduces your deduction to £8279.50
The childcare costs look low for £250 per week, but you haven't given details...you might want to query it. I think 211 days of £250 week childcare is more like £5k after the 70%, but I might be wrong. But they've taken your £8279.50 and knocked that off the childcare costs, so no child care help for you. That lowers your deduction to £3621.21 now.
So then child tax credits. 2 qualifying children (2 x £2781.30) plus the family element of £547.50 = 6110.10, take away your remaining deduction, and you actually get some money: £2488.89.
The figures don't align precisely, but that's the way it works.