at 10:11:37 AM
I've just read the other reply posts and I disagree with posters with all due respect (we get this kind of misinformation given to clients all the time). We move these toilets regularly in our bathroom restyles by drilling through the joists. You need a 4"dia hole, given that you have 2x10 there is stiil lots of meat on joists (3"top and bottom of hole) and most of joist load is carried at top and bottom of joists, just ask a structural engineer this and they will agree.
Now you have to keep "slope" or fall of the pipe in mind so keep a short bubble level handy. I notice that you have a heat duct run in same joist cavity, is this why you are moving toilet closet flange? If not and you are wanting to move toilet to allow for different floorplan I understand.
Once you have your new location mapped out for toilet mark your joists on top to indicate drill locations you will need about .75" of fall for that distance over 32 iinches if your joists are 16"on centre. You will have to double up each joist (the full span of bathroom) you cut through, this is recommended to give additional strength and you will glue and screw or power nail new joist material on. Use PL premium polyurethane adhesive to glue joists. just dont put glue where you are going to drill hole or you will gum up your drill bit with glue. Also you will need to put solid blockers on either sides of hole between joists to tie all joists together transferring loads to additional joists. You should put peices of wood between joists anyway as you will get a better floor. Use 3' spacing. You can use 2x10pcs, this will transfer loads between joists. Builders do not install as this takes too much time but you should do this anyway, we do it on all our floors and it gives super strength to structure.
As I said if you do this and clad your floor with .75" ply you end up with a super strong "deflection free" floor. Make sure you know your roughin dimension for toilet from wall, generally use 13" from wall stud, this should give you 12" finished for the toilet roughin, however some toilets require different roughin dimensions, just verify what toilet you will be using.
Also, I cant see the vent from toilet pipe so if you are further than 5' from stack you need to vent this toilet and tie vent to stack above in attic.