let 2 digit the number be

10a1 + a0, where a1 and a0 are the digits, a1,a0 >0

the number obtained by reversing the digits is 10a0 + a1

7 times a 2 digit number id equal to 4 times the number obtained by reversing the digits

7(10a1 + a0) = 4(10a0 + a1)

the difference between the digits is 1

|a1 - a0| = 1

First case when a1 - a0 = 1

by solving the system of equations

7(10a1 + a0) = 4(10a0 + a1)

a1 - a0 = 1

we find

a1 = -1

a0 = -2

and indeed the number -12 satisfies

7*(-12) = 4*(-21)

-84 = -84

Second case when a0 - a1 = 1

by solving the system of equations

7(10a1 + a0) = 4(10a0 + a1)

a0 - a1 = 1

we find

a1 = 1

a0 = 2

and indeed the number 12 satisfies

7*(12) = 4*(21)

84 = 84

there are two numbers that are solutions for this problem: 12 and -12.