I am trying to locate the following: Engine Zone Control Cable #851664
This is for a Sears Craftsman mower 4.0 HP 20" Cut.
According to Sears, the part is no longer available and I have been unable
to find it elsewhere. Is there an equivalent I can use? Can I just measure
and find something with the same dimensions?
Thanks in advance.

The #'s been superseded but still un-available:
https://www.partstree.com/parts/husqvarna-851664/ 
 
This is the engine brake/kill switch assembly correct, not a throttle?
 
.

Thank you for replying, Scott.
Yes, the cable is for the brake/kill switch assembly.
Do you know if there is an equivalent and where
I might be able to find it?

Even thou that specific cable is discontinued, it's the same design as later mowers.
Yours is probably a different  length.
 
You can put a longer, available one, on your mower .  I believe your engine is a Briggs so 
stick with that for lower engine end.
 
Look on E Bay as there's MANY cables.  The engine end is usually the same, the end 
at the handle is often different.  
 
If yours is not self propelled, it'll be much simpler to modify your handle (drill a hole)
for the new cable....
 
.

IE, this one would likely fit but you'll have to drill the handle AND in the exact location.
Of course measure the overall length.
 
https://www.ebay.com/itm/166288023469?_trksid=p2332490.c101196.m2219&itmprp=cksum%3A16628802346942b4cc30c731421fbb7a39c6d74bff5b%7Cenc%3AAQAKAAABQKf%252BZDynwIBzPFOUXzsYfl6V00AKQ%252B%252B7P%252BQrUe%252FaNcA%252F6g5%252BKJDCW80yl3sDyiOtDc%252Bwp382udDvnYxF7ZDSjYqJm5GyOUkm75MegRvdMcZOp66%252FyDudCANRlWAoDDDX9ZRRs6eeKMxk14INBi2LsIotdlYu3eCqDenizRyoqhRkHevVqt3cMsAnH4lRnRf52ekagziyIhcVLEdC9%252Bv%252FZ5C5XZkpHBmKB1hZtwF6LuYakXhkycBzY0GMsWtHWTVsx7UdeQBA3Q7FM3UAM79jB8C%252FLz2s37AHKXfrywCqai%252Fl3UN9AJAi3bFgqL7FDRqLgiHhLgW0wEAMErWB4ddDMdxiVSlQ%252FSa6x8arVupOukC2I4AaOynpC8QgUut44Yzlew1e3iioU4W53nQhk7GBoZ9dTClUnUhiT6fqjkflnjj9%7Campid%3APL_CLK%7Cclp%3A2332490&itmmeta=01JW66ME1MKW4MQ2EY1A67VFW2  
 

Thank you very much for the info! I will try it and let you know the outcome.

I tried a cable (Part #700892) off a Sears Pacesetter Eager-1 Model no. 917 872822 and it works perfectly.