History homework helper

Jelly,  17  16 bytes

DUµn/TṪṁ@Ṫ,j”-FṚ

A full program taking a list of years from, to and printing the result.

Try it online! or see the test suite.

How?

DUµn/TṪṁ@Ṫ,j”-FṚ - Main link: list of years [from, to]    e.g [1833,1871]
D                - convert to decimals                        [[1,8,3,3],[1,8,7,1]]
 U               - upend (to cater for differing lengths)     [[3,3,8,1],[1,7,8,1]]
  µ              - monadic chain separation, call that V
    /            - reduce V with:
   n             -   not equal?                               [1,1,0,0]
     T           - truthy indices                             [1, 2]
      Ṫ          - tail                                       2
         Ṫ       - tail V (pop from & modify V)               [1,7,8,1]
       ṁ@        - mould (swap @rguments) V like that length  [1,7]
          ,      - pair that with (the modified) V            [[1,7],[[3,3,8,1]]
            ”-   - literal '-' character
           j     - join                                       [1,7,'-',[3,3,8,1]]
              F  - flatten                                    [1,7,'-',3,3,8,1]
               Ṛ - reverse                                    [1,8,3,3,'-',7,1]
                 - implicit print                             1833-71

Javascript ES6, 59 57 chars

(x,y)=>(x+'-'+y).replace(x*10>y?/^((.*).*-)\2/:/()/,"$1")

Test:

f=(x,y)=>(x+'-'+y).replace(x*10>y?/^((.*).*-)\2/:/()/,"$1")

console.log(`1505, 1516 -> 1505-16
1989, 1991 -> 1989-91
1914, 1918 -> 1914-8
1833, 1871 -> 1833-71
1000, 2000 -> 1000-2000
1776, 2017 -> 1776-2017
2016, 2016 -> 2016-
1234567890, 1234567891 -> 1234567890-1
600, 1600 -> 600-1600
1235, 1424 -> 1235-424`.split`
`.map(t => t.match(/(\d+), (\d+) -> (.*)/)).every(([m,x,y,key]) => f(x,y)===key || console.log(x,y,key,f(x,y))))
console.log(f(600,6000))