Problem:

Counting the total number of times each of the substrings listed in column B appears within any of the strings in column A.

Solution:

Use the SUMPRODUCT, LEN, and SUBSTITUTE functions as shown in the following formula:
=SUMPRODUCT(LEN($A$2:$A$6)- LEN(SUBSTITUTE($A$2:$A$6,B2,\" \")))/LEN(B2)