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It says right in the error what went wrong.

rostopic: error: Argument error: while scanning a plain scalar
  in "<string>", line 1, column 16:
    {layout:{dim:[{label:'', size:0, stride:0}], da ... 
                   ^
found unexpected ':'
  in "<string>", line 1, column 21:
    {layout:{dim:[{label:'', size:0, stride:0}], data_of ...

This is saying that you need surround each one of your keys in single quotes '. What you should be typing is this:

rostopic pub motor/speed std_msgs/Int16MultiArray "{'layout':{'dim':[{'label':'', 'size':0, 'stride':0}], 'data_offset':0}, 'data':[64, 64]}"

It says right in the error what went wrong.

rostopic: error: Argument error: while scanning a plain scalar
  in "<string>", line 1, column 16:
    {layout:{dim:[{label:'', size:0, stride:0}], da ... 
                   ^
found unexpected ':'
  in "<string>", line 1, column 21:
    {layout:{dim:[{label:'', size:0, stride:0}], data_of ...

This is saying that you need surround each one of your keys in single quotes '. What you should be typing is this:

rostopic pub motor/speed std_msgs/Int16MultiArray "{'layout':{'dim':[{'label':'', 'size':0, 'stride':0}], 'data_offset':0}, 'data':[64, 64]}"

$ rostopipub motor/speed std_msgs/Int16MultiArray "layout:
  dim:
  - label: ''
    size: 0
    stride: 0
  data_offset: 0
data:
- 0"

It says right in the error what went wrong.

rostopic: error: Argument error: while scanning a plain scalar
  in "<string>", line 1, column 16:
    {layout:{dim:[{label:'', size:0, stride:0}], da ... 
                   ^
found unexpected ':'
  in "<string>", line 1, column 21:
    {layout:{dim:[{label:'', size:0, stride:0}], data_of ...

This is saying that you need surround each one of your keys in single quotes '. put a space between the colon : and the value. What you should be typing is this:

rostopic pub motor/speed std_msgs/Int16MultiArray "{'layout':{'dim':[{'label':'', 'size':0, 'stride':0}], 'data_offset':0}, 'data':[64, "{layout: {dim: [{label: '', size: 0, stride: 0}], data_offset: 0}, data: [64, 64]}"

A useful tip is that you should be using the tab autocomplete. If you use that, it will fill in the message with a nicely formatted YAML string like so:

$ rostopipub motor/speed std_msgs/Int16MultiArray "layout:
  dim:
  - label: ''
    size: 0
    stride: 0
  data_offset: 0
data:
- 0"

Then you can go into the string itself and enter your data.