Solution:-

Let us assume that, ∆ABC ~ ∆DEF

∆ABC is BC = 6cm

∆ABC ~ ∆DEF

So, AB/DE = BC/EF = AC/DF

Consider AB/DE = BC/EF

AB/8 = 6/4

AB = (6 × 8)/4

AB = 48/4

AB = 12

Now, consider BC/EF = AC/DF

6/4 = AC/7

AC = (6 × 7)/4

AC = 42/4

AC = 21/2

AC = 10.5 cm