To find out how much money Doug has for Free Agents this year, we would take his Projected Balance and add his CASH (which in-game is known as starting balance). So doug has a Projected Balance of $85,283,588 and $90,789,814 in CASH as his starting balance. He has so far, not offered any additional contracts (this is something you'd have to know about your own team, as it doesn't show up on the website).
So the equation would look like this:
85,283,588 + 90,789,814 - 0 = $176,073,402 for Free Agents.
What does that mean? All the contracts that Doug offers have to equal less then or equal to $176,073,402 in year one.
So you'd add up the year one value of the all contracts offers, and subtract that number from the $ for Free Agents. If it's positive, you're good.
Say Doug wanted to offer Player A a 2 year contract worth 25M per year. That contract (with a total value of $50M) would count 25M towards his Free Agent money.
Now...Contract Extension Money
The game says:
Current Budget - Projected Payroll for next year = $ for Extensions.
Notice that Cash does NOT enter into this equation at all. This is how the game calculates it.
For example, Doug has a Current Budget of $150,620,788 and the total of his projected salary for next year is $45.3M.