Answer:
4.5, you've got it right.
Explanation:
Best way to explain it is that you've got 3 right triangles. ABC, ACD, and CBD. Because line CD is perpendicular to line AB, as evidenced by <CDB, that means that all of these triangles are similar to each other. They have the same angle measures, and their side lengths maintain the same ratios. Since triangle ACD has a leg length of 8 and a leg length of 6, and in triangle CBD the leg length of 6 corresponds to the leg length of 8 in terms of ratio, then the dilation factor of triangle CBD is 3/4 (a lot of the math for this and everything else mentioned above is part of trigonometry and triangle proofs. if you don't know what those are, be thankful. they're some form of torture, i'm sure of it. if you do need to know all of it, lemme know and I'll try to revise my answer to include it).
Since 6 is 3/4ths of 8, you'd have to assume that whatever x is is 3/4ths of 6. Multiply 6 by 3/4, and you get 9/2, or 4.5.
Hope this was helpful!