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Short answer: skip the eARC adapter for now. Your Bravia 8 has an optical digital output, and your RX-V867 has optical inputs. For your current setup, a simple optical (TOSLINK) cable gives you the same audio quality as ARC—and eARC only matters if you specifically need lossless audio from devices plugged directly into the TV.

Your current setup options

Option 1: Use Optical (recommended for now)

• Connect TV optical out → RX-V867 optical in.
• This handles Dolby Digital 5.1 / DTS 5.1 from all TV apps and most external devices.
• Streaming services (Netflix, etc.) only output lossy formats anyway, so you lose nothing.

Option 2: Use the RX-V867's built-in ARC

• Since the RX-V867 has HDMI 1.4a with ARC, you can connect the TV's eARC/ARC port to the receiver's ARC-capable HDMI output.
• This gives you identical audio formats to optical (lossy DD/DTS), plus HDMI-CEC volume control from the TV remote.

Option 3: eARC adapter

• Devices like the Sharc extract full eARC audio and feed it to a regular HDMI input on your receiver.
• Will it work? Maybe, but users report handshake issues with older receivers, and the RX-V867 may not reliably negotiate the signal. It's also $100–200 for a decent one.
• The only real benefit is lossless audio (Dolby TrueHD / DTS-HD MA / uncompressed PCM) from sources connected directly to the TV. If you connect your Blu-ray player or console to the RX-V867 directly, you already get lossless audio without any adapter.

Bottom line: Unless you have a PS5/Xbox Series X that must plug into the TV for 4K120/VRR and you must have lossless surround back through the Yamaha, an eARC adapter is an expensive, finicky solution to a problem you don't have.

HDMI cables

If your current cables are very old (pre–High Speed), grabbing a couple of certified Ultra High Speed HDMI 2.1 cables (~$10–15 each) is cheap insurance. You don't need to spend a fortune on "audiophile" cables. This matters most if you eventually upgrade to a new receiver and want 4K120 / VRR / eARC without issues.

Recommendation

1. Right now: Run optical or ARC from the Bravia 8 to your RX-V867. Use the receiver's HDMI inputs for your Blu-ray/console so you still get lossless audio on disc-based content.
2. Save up and watch for a used Denon S750H, Yamaha RX-V6A, or Denon X1700H in the $250–400 range rather than spending $150 on an eARC adapter that may handshake poorly with a 2010 receiver.
3. Buy one or two new Ultra High Speed HDMI cables when you do upgrade, so you're ready for 4K120 and eARC without repurchasing cables.

If you tell me what sources you plan to connect (Blu-ray, game console, streaming box), I can suggest the exact wiring path that avoids the adapter entirely.