FYI - The attached diagram shows the basic method used to determine if a deck can support any load above the basic 10 psf dead load and 40 psf live load prescribed by code. The hot tub in your photo will have an impact on the section of deck depicted in the diagram. If the added load, in this case the hot tub, was supported on blocks or four legs that would concentrate the load in a very small area, then you would start by checking the deck boards to see if they could carry the concentrated load. Most hot tubs spread the load over the whole bottom area, so you can skip #1.
Start by placing 10 psf dead load over Area 1 & 2 plus 40 psf live load over Area 1 & 2, then add the weight of the hot tub over the foot print of the tub in Area 1. Using 40 psf live load over the entire deck would be more than enough to account for people in the tub.
Check the joists under the hot tub, if they pass, check the joist hangers on the tub side of beam AB and beam CD. Next check the design of beams AB & CD. Next check the load capacity of the post connections at A, B, C & D. Finish up by checking the load capacity of posts A, B, C & D, followed by the footing under each post.
The load carrying capacity will be limited by the weakest link in the load path from the deck boards down to the footings.