4 3/10 can be written as an improper fraction
color(white)("XXX")(4xx10+3)/10=43/10
3 3/5 can be written as an improper fraction
color(white)("XXX")(3xx5+3)/5=(18/5)
18/5 can be written with a denominator of 10 to match the 4 3/10=43/10 term
color(white)("XXX")(18xx2)/(5xx2)=36/10
Therefore
color(white)("XXX")4 3/10 - 3 3/5
is equivalent to
color(white)("XXX")43/10 - 36/10
color(white)("XXX")=7/10