Hi, Mark!
JMP 11.0 and higher has many options for analyzing multiple response (i.e. "Check all that apply" questions) in the Categorical platform.
For your data, you will want a column that specifies how many people responded to your survey. We call that a "sample size" column. If you don't have a column like that, you can create it using a formula or by just typing the appropriate sample size (number of survey respondents) for each year into the data table.
Once you have sample size, you can bring up the Categorical platform by selecting Analyze-> Consumer Research -> Categorical.
If I understand how your data is organized correctly, you'll want to follow these steps:
Once you are in the Categorical platform, select the "Multiple Response" tab.
1) Shift-select to select all of the columns that have your counts.
2) Click the "Response Frequencies" button.
3) Assign the "Year" column (2013 vs 2014) to the X role (bottom center).
4) Assign your Sample Size column (described above) to the Sample Size role.
4) Click "OK"
The resulting report should compare the response frequencies for each column, treating them all as one variable.
There's additional documentation on Response Frequencies (with an example) here: Additional Examples of the Categorical Platform.
That page also contains more information about Multiple Response columns in JMP.
Please respond if you have more questions!
Best,
Melinda