Note that the 6 digit base 14 number can be written Cx95Dy

(p&p below)

A short program finds only [7, 6]

C795D6 base 14 is 6748664 base 10

def base2base(n,a,b):
    """ input n which is a string of the number to be changed
    'a' is an integer representing the current base
    to be changed to base b
    """
    def dec2base(i,base):
        """ INPUT integer in base 10, return string
        of Base base equivalent. """
        convertString = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
        if i < base:
            return convertString[i]
        else:
            return dec2base(i//base,base) + convertString[i%base]
    if a == 10:
        return dec2base(int(n),b)
    if b == 10:
        return int(str(n),a)
    elif b != 10:
        return base2base(int(str(n),a),10,b)

xyvalues = []
for x in range(14):
    for y in range(14):
        # if (537824*x + y)%104 == 78:
        if (40*x + y)%104 == 78:
            xyvalues.append([x,y])

for pair in xyvalues:
    num14 = 'C' + str(pair[0]) + '95D' + str(pair[1])
    num10 = base2base(num14, 14, 10)
    print(pair, num10%104)

--------

Analytic solution:

76 base 14 is 104 base 10.
C095D0 base 14 is 6479746 base 10.
mod(6479746, 104) is 26
Cx95Dy base 14 represents our mystery number.
x000y base 14 must be 78 + 104k so that Cx95Dy base 14 is divisible by 76 base 14
14**5 is 537824
x000y base 14 is 537824x + y = 78 + 104k
or  mod((537824x + y),104) = 78
mod(537824,104) = 40
mod((40x + y),104) = 78
40x + y = 78 + 104k
max LHS is 533,   So k is in {0,1,2,3,4}  
and RHS is in {78,182,286,390,494}
Since 40x ends in 0, y is in {0,2,4,6,8}
RHS minus corresponding y value:  {70,180,280,390,490}
but of these, only 280 is divisible by 40
thus RHS is 286, x is 7, y is 6