The model is given as:
ytβ=0.2ΓTimetβ+10.5+3.0ΓD2tβ+5.4ΓD3tβ+0.7ΓD4tβ
Since y(T+1)β refers to June 2019, September 2020 corresponds to y(T+16)β (16 periods later).
September falls under the fourth quarter dummy D4tβ (since D4β = 1 for Q4, and 0 otherwise).
Plugging into the model:
y(T+16)β=0.2Γ16+10.5+0.7Γ1
=3.2+10.5+0.7
=14.4
Thus, the model predicts 14,400 housing starts in September 2020.