Help me get the day of the week correct
JavaScript (ES6), 48 bytes
Expects (day1)(day2).
a=&gt;b=&gt;((g=s=&gt;parseInt(s,34)%72%23)(a)-g(b)+21)%7

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How?
We need a hash function \$g\$ that turns a day string into an index. The results of this function are actually quite flexible:

They can be in ascending or descending order: 0,1,2,3,4,5,6 or 6,5,4,3,2,1,0. (We'll have to compute either \$g(a)-g(b)\$ or \$g(b)-g(a)\$ accordingly.)
Day #0 may be any day of the week. For instance, 3,4,5,6,0,1,2 or 4,3,2,1,0,6,5 are also valid.
The results may be greater than \$6\$ as long as they are correct modulo \$7\$. Because the sign of the modulo is the sign of the dividend in JS, we'll have to do something like (g(a) - g(b) + k) % 7 anyway, where \$k\$ is a large enough multiple of \$7\$.

The following function was found by brute-force:
g = s =&gt; parseInt(s, 34) % 72 % 23

which gives:
 day         | base34 -&gt; dec | mod 72 | mod 23 | mod 7
-------------+---------------+--------+--------+-------
 &quot;Monday&quot;    |      30369728 |   56   |   10   |   3
 &quot;Tuesday&quot;   |    1358300452 |    4   |    4   |   4
 &quot;Wednesday&quot; | 1702996445748 |   12   |   12   |   5
 &quot;Thursday&quot;  |   45612914380 |   52   |    6   |   6
 &quot;Friday&quot;    |      21127508 |   44   |   21   |   0
 &quot;Saturday&quot;  |   43748842416 |   24   |    1   |   1
 &quot;Sunday&quot;    |      38623568 |   32   |    9   |   2