Which type for 4 unit bridge you recommend on back molar teeth #11 to 14. is it crown- porcelain fused to high noble metal, gold, or pure porcelain.?

Depends on the need: The types of materials that i chose for my patient is dependent on the occlusion (bite) the types of dental material or natural tooth on the opposing tooth structure and the force of the bite. Any and all of those choices and their combination could be right.

Depends: #11 thru 13 could be porcelain fused to high noble metal & #14 gold (high noble metal or all porcelain fused to metal. All gold would be very unesthetic. Would not recommend pure porcelain, although some ceramic materials might be used to replace just one tooth. More than one missing tooth might flex and break.

Porc - High Noble: I would recommend implants before this long span bridge involving the canine. Is this an option ? Otherwise, the porc - high noble is my recommendation for fit and esthetics.

See below: Your bridge involves replacing two missing teeth. If the teeth on either side of the missing ones are healthy, i would strongly suggest you have implants done rather then cutting down to healthy teeth. If that is not an option you can use porelcain to gold but i would use a zirconium bridge. They are very strong and without metal.

Usually would not: The biggest concern is the length of the span. Gold is unaestheitc and soft. The pfm bridge could flex and the porcelain could crack. Some of the new ceramics could work, but have you ruled out implants?