let x and x+1 be the two consecutive integers where x is integer

x*(x+1) = 4(x + x + 1) - 10

x^2 + x = 8x + 4 - 10

x^2 + x - 8x + 6 = 0

x^2 - 7x + 6 = 0

by solving the quadratic equation we find 2 solutions

x1 = 6

x2 = 1

thus we have 2 solutions for the problem

the two consecutive integers can be 6 and 7 and indeed 6*7 = 4(6 + 7) - 10

the two consecutive integers can be 1 and 2 and indeed 1*2 = 4(1 + 2) - 10