Adafruit_ADXL343.h: No such file or directory

Arduino: 1.8.9 (Mac OS X), Board: "Arduino Ethernet"

Multiple libraries were found for "Adafruit_Sensor.h"
Used: /Users/imac/Documents/Arduino/libraries/Adafruit_Sensor
Not used: /Users/imac/Documents/Arduino/libraries/Adafruit_Unified_Sensor
sensortest:3:30: error: Adafruit_ADXL343.h: No such file or directory
compilation terminated.
exit status 1
Adafruit_ADXL343.h: No such file or directory

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Did you install the ADXL345 library?
https://learn.adafruit.com/adxl343-breakout-learning-guide/arduino#installation-3018247-6

I installed the ADXL library, but still get this:

Arduino: 1.8.9 (Mac OS X), Board: "Arduino Ethernet"

In file included from /Users/imac/Documents/Arduino/libraries/Adafruit_ADXL343/examples/sensortest/sensortest.ino:3:0:
/Users/imac/Documents/Arduino/libraries/Adafruit_ADXL343/Adafruit_ADXL343.h:27:37: fatal error: Adafruit_BusIO_Register.h: No such file or directory
compilation terminated.
exit status 1
Error compiling for board Arduino Ethernet.

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Install it via Library Manager so dependencies are taken care of:
https://github.com/adafruit/Adafruit_ADXL343/blob/bf29bba97ef1a984201036a8e1eba4976b1df34e/library.properties#L10
You may also need to update your Arduino IDE. The library dependency feature was added at 1.8.10:
https://github.com/arduino/Arduino/releases/tag/1.8.10

Installed via Library Manager, and I have now updated my IDE.

Getting this now:

Arduino: 1.8.15 (Mac OS X), Board: "Arduino Ethernet"

In file included from /Users/imac/Documents/Arduino/libraries/Adafruit_ADXL343/examples/sensortest/sensortest.ino:3:0:
/Users/imac/Documents/Arduino/libraries/Adafruit_ADXL343/Adafruit_ADXL343.h:27:10: fatal error: Adafruit_BusIO_Register.h: No such file or directory
#include <Adafruit_BusIO_Register.h>
^~~~~~~~~~~~~~~~~~~~~~~~~~~
compilation terminated.
exit status 1
Error compiling for board Arduino Ethernet.

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Same error. Since you previously tried to install it with the older version, simply updating may not be dealing with dependencies correctly. It may be assuming they are already taken care of. Try installing the BusIO library via Library Manager:
https://github.com/adafruit/Adafruit_BusIO

Tried that, now giving me this:

Arduino: 1.8.15 (Mac OS X), Board: "Arduino Ethernet"

/Users/imac/Documents/Arduino/libraries/Adafruit_ADXL343/examples/sensortest/sensortest.ino: In function 'void setup()':
sensortest:128:9: error: 'class Adafruit_ADXL343' has no member named 'printSensorDetails'
accel.printSensorDetails();
^~~~~~~~~~~~~~~~~~
exit status 1
'class Adafruit_ADXL343' has no member named 'printSensorDetails'

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Unknown. Something just seems mixed up with your library installs. That method gets inherited from the sensor lib:

Adafruit_Sensor/Adafruit_Sensor.h

Line 182 in 6cea0d9

void printSensorDetails(void);