Trying to Create A Slicer

Chaucer You could do this via a Complex Slicer by using searching (SEARCH) or CONTAINS and return 1 or 0 whether to display or not. 

https://community.powerbi.com/t5/Quick-Measures-Gallery/The-Complex-Selector/m-p/1116633#M534

Like:

Flag Measure =
  VAR __Slicer = SELECTEDVALUE('Slicer'[Column])
RETURN
  IF(SEARCH(__Slicer,'Table'[Column],,0)>0,1,0)

Chaucer 

Ok, so here are the steps:

1) Original table:

 2) Select the Characteristics column and use the "Split Column" function in the ribbon, Choose "comma" as the delimiter:

3) Select the Product column, choose the Unpivot function in the ribbon and select "Unpivot other columns"

4) Remove the "Attribute" Column:

5) Rename the remaining columns. You might also want to clear up the new Characteristics column just in case: select it, go to the Transform tab , select Format in the ribbon and select "Trim" and then "Clean"

 6) Create a new table by referencing the Products table (I've called this new table "Slicer Characteristics"):

 7) Remove the "Products column" from this new table (Slicer Characteristics)

'8) Remove Duplicates from the remaining "Chracteristics" column:

9) load into the model, and create a one-to-many relationship between the "Slicer Characteristics" table and the Products Table:

10) Create a measure to list the selected characteristics to use in your table visual:

Selected Characteristics = 
VAR Charact = CONCATENATEX(VALUES('PB Products'[Characteristics]), 
'PB Products'[Characteristics], ", ")
RETURN
IF(ISINSCOPE('PB Products'[Product]), Charact)

And this is what you get:

If you want to include the other characteristics associated to the filtered products, you can use this measure:

Other associated Characteristics = 
VAR full = CALCULATETABLE(VALUES('PB Products'[Characteristics]), ALLEXCEPT('PB Products','PB Products'[Product]))
VAR Selected = VALUES('PB Products'[Characteristics])
VAR List = CONCATENATEX(EXCEPT(full, Selected),  'PB Products'[Characteristics], ", ")
RETURN
IF(ISBLANK([Selected Characteristics]), BLANK(), List)

Which gets you this:

If you wish to include the full list of Characteristics for the filtered products (instead of separate columns), you can use:

Full Characteristics (filtered) = 
VAR full = CALCULATETABLE(VALUES('PB Products'[Characteristics]), ALLEXCEPT('PB Products','PB Products'[Product]))
VAR List = CONCATENATEX(full,  'PB Products'[Characteristics], ", ")
RETURN
IF(ISBLANK([Selected Characteristics]), BLANK(), List)

I've included the PBIX file for your reference.