There may be some confusion in terminology. If the total cost of your project is $12K, then you would be asking ITIF for no more than 50% ($6K)
(As an aside, you don’t always have to ask for 50% of the cost (e.g., if the total cost of your project is $12K, and you have another source that will give you $8K, then you only need to ask ITIF for the remain $4k). Many project proposals suffer from an obvious false inflation of the estimated cost to be exactly double the maximum one can ask for. The proposer should first get an accurate estimate of the true cost of the project, and then only ask for half of that.