How can I solve this?

Let's first write the input and output using decimals:

x | y

0 | 0

1 | 1

2 | 2

3 | 3

4 | 4

5 | 5

6 | 6

7 | 0

8 | 1

9 | 2

Now write it as bits. 

The input can be 0-9 which requires 4 bits.

The output is 0-6 which requires 3 bits.

x3 x2 x1 x0 | y2 y1 y0

0 0 0 0 | 0 0 0

0 0 0 1 | 0 0 1

0 0 1 0 | 0 1 0

0 0 1 1 | 0 1 1

0 1 0 0 | 1 0 0

0 1 0 1 | 1 0 1

0 1 1 0 | 1 1 0

0 1 1 1 | 0 0 0

1 0 0 0 | 0 0 1

1 0 0 1 | 0 1 0

1 0 1 0 | x x x

1 0 1 1 | x x x

1 1 0 0 | x x x

1 1 0 1 | x x x

1 1 1 0 | x x x

1 1 1 1 | x x x

The rows for 10 to 15 have "don't care" values for the outputs because we should only ever get 0-9 as an input.

Now solve for each of the 3 bits in the output, using Karnaugh maps and build the reduced circuit.